R : Copyright 2005, The R Foundation for Statistical Computing
Version 2.1.1  (2005-06-20), ISBN 3-900051-07-0

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for a HTML browser interface to help.
Type 'q()' to quit R.

> ### * <HEADER>
> ###
> attach(NULL, name = "CheckExEnv")
> assign(".CheckExEnv", as.environment(2), pos = length(search())) # base
> ## add some hooks to label plot pages for base and grid graphics
> setHook("plot.new", ".newplot.hook")
> setHook("persp", ".newplot.hook")
> setHook("grid.newpage", ".gridplot.hook")
> 
> assign("cleanEx",
+        function(env = .GlobalEnv) {
+ 	   rm(list = ls(envir = env, all.names = TRUE), envir = env)
+            RNGkind("default", "default")
+ 	   set.seed(1)
+    	   options(warn = 1)
+ 	   delayedAssign("T", stop("T used instead of TRUE"),
+ 		  assign.env = .CheckExEnv)
+ 	   delayedAssign("F", stop("F used instead of FALSE"),
+ 		  assign.env = .CheckExEnv)
+ 	   sch <- search()
+ 	   newitems <- sch[! sch %in% .oldSearch]
+ 	   for(item in rev(newitems))
+                eval(substitute(detach(item), list(item=item)))
+ 	   missitems <- .oldSearch[! .oldSearch %in% sch]
+ 	   if(length(missitems))
+ 	       warning("items ", paste(missitems, collapse=", "),
+ 		       " have been removed from the search path")
+        },
+        env = .CheckExEnv)
> assign("..nameEx", "__{must remake R-ex/*.R}__", env = .CheckExEnv) # for now
> assign("ptime", proc.time(), env = .CheckExEnv)
> grDevices::postscript("spdep-Examples.ps")
> assign("par.postscript", graphics::par(no.readonly = TRUE), env = .CheckExEnv)
> options(contrasts = c(unordered = "contr.treatment", ordered = "contr.poly"))
> options(warn = 1)    
> library('spdep')
Loading required package: tripack
Loading required package: maptools
Loading required package: foreign
Loading required package: SparseM
[1] "SparseM library loaded"
> 
> assign(".oldSearch", search(), env = .CheckExEnv)
> assign(".oldNS", loadedNamespaces(), env = .CheckExEnv)
> cleanEx(); ..nameEx <- "EBImoran.mc"
> 
> ### * EBImoran.mc
> 
> flush(stderr()); flush(stdout())
> 
> ### Encoding: latin1
> 
> ### Name: EBImoran.mc
> ### Title: Permutation test for empirical Bayes index
> ### Aliases: EBImoran.mc EBImoran
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(nc.sids)
> EBImoran.mc(spNamedVec("SID74", nc.sids), spNamedVec("BIR74", nc.sids),
+  nb2listw(ncCC89.nb, style="B", zero.policy=TRUE), nsim=999,
+  zero.policy=TRUE)

	Monte-Carlo simulation of Empirical Bayes Index

data:  cases: spNamedVec("SID74", nc.sids), risk population: spNamedVec("BIR74", nc.sids)
weights: nb2listw(ncCC89.nb, style = "B", zero.policy = TRUE)
number of simulations + 1: 1000
 
statistic = 0.254, observed rank = 1000, p-value = 0.001
alternative hypothesis: greater 

> sids.p <- nc.sids$SID74 / nc.sids$BIR74
> names(sids.p) <- rownames(nc.sids)
> moran.mc(sids.p, nb2listw(ncCC89.nb, style="B", zero.policy=TRUE),
+  nsim=999, zero.policy=TRUE)

	Monte-Carlo simulation of Moran's I

data:  sids.p 
weights: nb2listw(ncCC89.nb, style = "B", zero.policy = TRUE)  
number of simulations + 1: 1000 
 
statistic = 0.2133, observed rank = 999, p-value = 0.001
alternative hypothesis: greater 

> 
> 
> 
> cleanEx(); ..nameEx <- "EBest"
> 
> ### * EBest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: EBest
> ### Title: Global Empirical Bayes estimator
> ### Aliases: EBest
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(auckland)
> res <- EBest(auckland$Deaths.1977.85, 9*auckland$Under.5.1981)
> attr(res, "parameters")
$a
[1] 7.284173e-07

$b
[1] 0.002633436

> cols <- grey(6:2/7)
> brks <- c(-Inf,2,2.5,3,3.5,Inf)
> library(maptools)
> plot(auckpolys, col=cols[findInterval(res$estmm*1000, brks)], forcefill=FALSE)
> legend(c(70,90), c(70,95), fill=cols, legend=leglabs(brks), bty="n")
> title(main="Global moment estimator of infant mortality per 1000 per year")
> 
> 
> 
> cleanEx(); ..nameEx <- "EBlocal"
> 
> ### * EBlocal
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: EBlocal
> ### Title: Local Empirical Bayes estimator
> ### Aliases: EBlocal
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(auckland)
> res <- EBlocal(spNamedVec("Deaths.1977.85", auckland),
+  9*spNamedVec("Under.5.1981", auckland), auckland.nb)
> brks <- c(-Inf,2,2.5,3,3.5,Inf)
> cols <- grey(6:2/7)
> library(maptools)
> plot(auckpolys, col=cols[findInterval(res$est*1000, brks)], forcefill=FALSE)
> legend(c(70,90), c(70,95), fill=cols, legend=leglabs(brks), bty="n")
> title(main="Local moment estimator of infant mortality per 1000 per year")
> 
> 
> 
> cleanEx(); ..nameEx <- "LR.sarlm"
> 
> ### * LR.sarlm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: LR.sarlm
> ### Title: Likelihood ratio test
> ### Aliases: LR.sarlm LR1.sarlm Wald1.sarlm logLik.sarlm
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> mixed <- lagsarlm(CRIME ~ HOVAL + INC, data=columbus, nb2listw(col.gal.nb),
+   type="mixed")
> error <- errorsarlm(CRIME ~ HOVAL + INC, data=columbus, nb2listw(col.gal.nb))
> LR.sarlm(mixed, error)

	Likelihood ratio for spatial linear models

data:  
Likelihood ratio = 4.2782, df = 2, p-value = 0.1178
sample estimates:
Log likelihood of mixed Log likelihood of error 
              -182.0161               -184.1552 

> 
> 
> 
> cleanEx(); ..nameEx <- "afcon"
> 
> ### * afcon
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: afcon
> ### Title: Spatial patterns of conflict in Africa 1966-78
> ### Aliases: afcon africa.rook.nb afxy paper.nb
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(afcon)
> plot(africa.rook.nb, afxy)
> plot(diffnb(paper.nb, africa.rook.nb), afxy, col="red", add=TRUE)
Neighbour difference for region id: MO in relation to id: MR 
Neighbour difference for region id: MR in relation to id: MO 
Neighbour difference for region id: CG in relation to id: TZ 
Neighbour difference for region id: TZ in relation to id: CG 
Neighbour difference for region id: AO in relation to id: SF 
Neighbour difference for region id: ZA in relation to id: BC SF 
Neighbour difference for region id: BC in relation to id: ZA 
Neighbour difference for region id: SF in relation to id: AO ZA 
> text(afxy, labels=attr(africa.rook.nb, "region.id"), pos=4, offset=0.4)
> moran.test(spNamedVec("totcon", afcon), nb2listw(africa.rook.nb))

	Moran's I test under randomisation

data:  spNamedVec("totcon", afcon)  
weights: nb2listw(africa.rook.nb)  
 
Moran I statistic standard deviate = 4.1251, p-value = 1.853e-05
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
       0.40981723       -0.02439024        0.01107950 

> moran.test(spNamedVec("totcon", afcon), nb2listw(paper.nb))

	Moran's I test under randomisation

data:  spNamedVec("totcon", afcon)  
weights: nb2listw(paper.nb)  
 
Moran I statistic standard deviate = 4.3485, p-value = 6.854e-06
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
       0.41679563       -0.02439024        0.01029358 

> geary.test(spNamedVec("totcon", afcon), nb2listw(paper.nb))

	Geary's C test under randomisation

data:  spNamedVec("totcon", afcon) 
weights: nb2listw(paper.nb) 
 
Geary C statistic standard deviate = -2.8988, p-value = 0.001873
alternative hypothesis: less 
sample estimates:
Geary C statistic       Expectation          Variance 
       0.58395772        1.00000000        0.02059931 

> 
> 
> 
> cleanEx(); ..nameEx <- "anova.sarlm"
> 
> ### * anova.sarlm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: anova.sarlm
> ### Title: Comparison of simultaneous autoregressive models
> ### Aliases: anova.sarlm
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> lm.mod <- lm(CRIME ~ HOVAL + INC, data=columbus)
> lag <- lagsarlm(CRIME ~ HOVAL + INC, data=columbus, nb2listw(col.gal.nb))
> mixed <- lagsarlm(CRIME ~ HOVAL + INC, data=columbus, nb2listw(col.gal.nb),
+   type="mixed")
> error <- errorsarlm(CRIME ~ HOVAL + INC, data=columbus, nb2listw(col.gal.nb))
> LR.sarlm(mixed, error)

	Likelihood ratio for spatial linear models

data:  
Likelihood ratio = 4.2782, df = 2, p-value = 0.1178
sample estimates:
Log likelihood of mixed Log likelihood of error 
              -182.0161               -184.1552 

> anova(lag, lm.mod)
       Model df      AIC    logLik   Test  L.Ratio     p-value
lag        1  5 376.3366 -183.1683              NA          NA
lm.mod     2  4 382.7545 -187.3772 1 vs 2 8.417918 0.003715411
> anova(lag, error, mixed)
      Model df      AIC    logLik   Test  L.Ratio   p-value
lag       1  5 376.3366 -183.1683              NA        NA
error     2  5 378.3104 -184.1552              NA        NA
mixed     3  7 378.0322 -182.0161 2 vs 3 4.278176 0.1177622
> AIC(lag, error, mixed)
      df      AIC
lag    5 376.3366
error  5 378.3104
mixed  7 378.0322
> 
> 
> 
> cleanEx(); ..nameEx <- "asMatrixCsrListw"
> 
> ### * asMatrixCsrListw
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: asMatrixCsrListw
> ### Title: Convert spatial weights list to CSR matrix form
> ### Aliases: asMatrixCsrListw asListwMatrixCsr asMatrixCsrIrW asMatrixCsrI
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> COL.W <- nb2listw(COL.nb, style="W")
> COL.W
Characteristics of weights list object:
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 232 
Percentage nonzero weights: 9.66264 
Average number of links: 4.734694 

Weights style: W 
Weights constants summary:
   n   nn S0       S1       S2
W 49 2401 49 23.29434 204.8729
> image(asMatrixCsrListw(COL.W))
> 
> 
> 
> cleanEx(); ..nameEx <- "baltimore"
> 
> ### * baltimore
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: baltimore
> ### Title: House sales prices, Baltimore, MD 1978
> ### Aliases: baltimore
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(baltimore)
> ## maybe str(baltimore) ; plot(baltimore) ...
> 
> 
> 
> cleanEx(); ..nameEx <- "boston"
> 
> ### * boston
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: boston
> ### Title: Corrected Boston Housing Data
> ### Aliases: boston.c boston boston.soi boston.utm
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(boston)
> hr0 <- lm(log(MEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + I(RM^2) +
+  AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT), data=boston.c)
> summary(hr0)

Call:
lm(formula = log(MEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + 
    I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + 
    log(LSTAT), data = boston.c)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.71176 -0.09169 -0.00566  0.09895  0.79780 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.558e+00  1.544e-01  29.512  < 2e-16 ***
CRIM        -1.186e-02  1.245e-03  -9.532  < 2e-16 ***
ZN           8.016e-05  5.056e-04   0.159 0.874105    
INDUS        2.395e-04  2.364e-03   0.101 0.919318    
CHAS1        9.140e-02  3.320e-02   2.753 0.006129 ** 
I(NOX^2)    -6.380e-01  1.131e-01  -5.639 2.88e-08 ***
I(RM^2)      6.328e-03  1.312e-03   4.823 1.89e-06 ***
AGE          9.074e-05  5.263e-04   0.172 0.863179    
log(DIS)    -1.913e-01  3.339e-02  -5.727 1.78e-08 ***
log(RAD)     9.571e-02  1.913e-02   5.002 7.91e-07 ***
TAX         -4.203e-04  1.227e-04  -3.426 0.000664 ***
PTRATIO     -3.112e-02  5.013e-03  -6.208 1.14e-09 ***
B            3.637e-04  1.031e-04   3.527 0.000460 ***
log(LSTAT)  -3.712e-01  2.501e-02 -14.841  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.1825 on 492 degrees of freedom
Multiple R-Squared: 0.8059,	Adjusted R-squared: 0.8008 
F-statistic: 157.1 on 13 and 492 DF,  p-value: < 2.2e-16 

> logLik(hr0)
'log Lik.' 149.9548 (df=15)
> gp0 <- lm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + I(RM^2) +
+  AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT), data=boston.c)
> summary(gp0)

Call:
lm(formula = log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + 
    I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + 
    log(LSTAT), data = boston.c)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.70893 -0.09295 -0.01049  0.09575  0.79618 

Coefficients:
              Estimate Std. Error t value Pr(>|t|)    
(Intercept)  4.562e+00  1.523e-01  29.955  < 2e-16 ***
CRIM        -1.177e-02  1.228e-03  -9.590  < 2e-16 ***
ZN           9.175e-05  4.987e-04   0.184 0.854085    
INDUS        1.789e-04  2.331e-03   0.077 0.938846    
CHAS1        9.213e-02  3.274e-02   2.813 0.005097 ** 
I(NOX^2)    -6.372e-01  1.116e-01  -5.711 1.95e-08 ***
I(RM^2)      6.255e-03  1.294e-03   4.833 1.80e-06 ***
AGE          7.100e-05  5.190e-04   0.137 0.891253    
log(DIS)    -1.978e-01  3.293e-02  -6.007 3.67e-09 ***
log(RAD)     8.957e-02  1.887e-02   4.746 2.72e-06 ***
TAX         -4.191e-04  1.210e-04  -3.464 0.000579 ***
PTRATIO     -2.960e-02  4.944e-03  -5.986 4.14e-09 ***
B            3.611e-04  1.017e-04   3.551 0.000421 ***
log(LSTAT)  -3.749e-01  2.466e-02 -15.200  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 0.1799 on 492 degrees of freedom
Multiple R-Squared: 0.8108,	Adjusted R-squared: 0.8058 
F-statistic: 162.1 on 13 and 492 DF,  p-value: < 2.2e-16 

> logLik(gp0)
'log Lik.' 156.9788 (df=15)
> lm.morantest(hr0, nb2listw(boston.soi))

	Global Moran's I for regression residuals

data:  
model: lm(formula = log(MEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) +
I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),
data = boston.c)
weights: nb2listw(boston.soi)
 
Moran I statistic standard deviate = 14.5085, p-value < 2.2e-16
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
      0.4364296993      -0.0168870829       0.0009762383 

> gp1 <- errorsarlm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + I(RM^2)
+  +  AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),
+  data=boston.c, nb2listw(boston.soi), method="SparseM", 
+  tol.opt = .Machine$double.eps^(1/4))
> summary(gp1)

Call:errorsarlm(formula = log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + 
    I(NOX^2) + I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + 
    B + log(LSTAT), data = boston.c, listw = nb2listw(boston.soi), 
    method = "SparseM", tol.opt = .Machine$double.eps^(1/4))

Residuals:
        Min          1Q      Median          3Q         Max 
-6.4315e-01 -6.7098e-02  7.1602e-05  7.5522e-02  6.5017e-01 

Type: error 
Coefficients: (asymptotic standard errors) 
               Estimate  Std. Error  z value  Pr(>|z|)
(Intercept)  3.8403e+00  1.5701e-01  24.4594 < 2.2e-16
CRIM        -5.2921e-03  9.4259e-04  -5.6145 1.972e-08
ZN           4.7295e-04  5.0495e-04   0.9366  0.348955
INDUS       -2.5159e-05  2.7607e-03  -0.0091  0.992729
CHAS1       -3.8824e-02  2.7525e-02  -1.4105  0.158386
I(NOX^2)    -2.2283e-01  1.5959e-01  -1.3963  0.162630
I(RM^2)      7.9634e-03  1.0319e-03   7.7174 1.177e-14
AGE         -1.0508e-03  4.8725e-04  -2.1566  0.031036
log(DIS)    -1.1752e-01  4.7439e-02  -2.4772  0.013242
log(RAD)     6.5538e-02  2.0605e-02   3.1806  0.001470
TAX         -4.9962e-04  1.1760e-04  -4.2485 2.152e-05
PTRATIO     -1.7664e-02  5.5099e-03  -3.2058  0.001347
B            5.9446e-04  1.0818e-04   5.4952 3.903e-08
log(LSTAT)  -2.6595e-01  2.2581e-02 -11.7780 < 2.2e-16

Lambda: 0.71548 LR test value: 224.9 p-value: < 2.22e-16 

Log likelihood: 269.4266 for error model
ML residual variance (sigma squared): 0.017012, (sigma: 0.13043)
Number of observations: 506 
Number of parameters estimated: 16 
AIC: -506.85, (AIC for lm: -283.96)

> gp2 <- lagsarlm(log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + I(RM^2)
+  +  AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + log(LSTAT),
+  data=boston.c, nb2listw(boston.soi), method="SparseM")
> summary(gp2)

Call:lagsarlm(formula = log(CMEDV) ~ CRIM + ZN + INDUS + CHAS + I(NOX^2) + 
    I(RM^2) + AGE + log(DIS) + log(RAD) + TAX + PTRATIO + B + 
    log(LSTAT), data = boston.c, listw = nb2listw(boston.soi), 
    method = "SparseM")

Residuals:
       Min         1Q     Median         3Q        Max 
-0.5262308 -0.0749699 -0.0044237  0.0713409  0.7122121 

Type: lag 
Coefficients: (log likelihood/likelihood ratio) 
               Estimate Log likelihood LR statistic  Pr(>|z|)
(Intercept)  2.2796e+00             NA           NA        NA
CRIM        -7.1045e-03     2.3884e+02      50.3390 1.294e-12
ZN           3.7985e-04     2.6352e+02       0.9715 0.3243010
INDUS        1.2572e-03     2.6377e+02       0.4877 0.4849681
CHAS1        7.3677e-03     2.6397e+02       0.0819 0.7746851
I(NOX^2)    -2.6892e-01     2.5943e+02       9.1619 0.0024710
I(RM^2)      6.7243e-03     2.4236e+02      43.2951 4.707e-11
AGE         -2.7682e-04     2.6377e+02       0.4762 0.4901358
log(DIS)    -1.5830e-01     2.4538e+02      37.2542 1.037e-09
log(RAD)     7.0689e-02     2.5252e+02      22.9730 1.643e-06
TAX         -3.6569e-04     2.5645e+02      15.1129 0.0001013
PTRATIO     -1.2011e-02     2.5940e+02       9.2264 0.0023854
B            2.8432e-04     2.5754e+02      12.9406 0.0003215
log(LSTAT)  -2.3216e-01     2.0587e+02     116.2822 < 2.2e-16

Rho: 0.48537 LR test value: 214.06 p-value: < 2.22e-16 

Log likelihood: 264.0089 for lag model
ML residual variance (sigma squared): 0.019276, (sigma: 0.13884)
Number of observations: 506 
Number of parameters estimated: 16 
AIC: -496.02, (AIC for lm: -283.96)

> 
> 
> 
> 
> cleanEx(); ..nameEx <- "bptest.sarlm"
> 
> ### * bptest.sarlm
> 
> flush(stderr()); flush(stdout())
> 
> ### Encoding: latin1
> 
> ### Name: bptest.sarlm
> ### Title: Breusch-Pagan test for spatial models
> ### Aliases: bptest.sarlm
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> error.col <- errorsarlm(CRIME ~ HOVAL + INC, data=columbus,
+  nb2listw(col.gal.nb))
> bptest.sarlm(error.col)

	studentized Breusch-Pagan test

data:  
BP = 9.3694, df = 2, p-value = 0.009235

> bptest.sarlm(error.col, studentize=FALSE)

	Breusch-Pagan test

data:  
BP = 16.2854, df = 2, p-value = 0.0002908

> 
> 
> 
> cleanEx(); ..nameEx <- "card"
> 
> ### * card
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: card
> ### Title: Cardinalities for neighbours lists
> ### Aliases: card
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> table(card(col.gal.nb))

 2  3  4  5  6  7  8  9 10 
 7  7 13  4  9  6  1  1  1 
> 
> 
> 
> cleanEx(); ..nameEx <- "cell2nb"
> 
> ### * cell2nb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: cell2nb
> ### Title: Generate neighbours list for grid cells
> ### Aliases: cell2nb mrc2vi rookcell queencell vi2mrc
> ### Keywords: spatial
> 
> ### ** Examples
> 
> nb7rt <- cell2nb(7, 7)
> summary(nb7rt)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 168 
Percentage nonzero weights: 6.997085 
Average number of links: 3.428571 
Link number distribution:

 2  3  4 
 4 20 25 
4 least connected regions:
1:1 7:1 1:7 7:7 with 2 links
25 most connected regions:
2:2 3:2 4:2 5:2 6:2 2:3 3:3 4:3 5:3 6:3 2:4 3:4 4:4 5:4 6:4 2:5 3:5 4:5 5:5 6:5 2:6 3:6 4:6 5:6 6:6 with 4 links
> xyc <- attr(nb7rt, "region.id")
> xy <- matrix(as.integer(unlist(strsplit(xyc, ":"))), ncol=2, byrow=TRUE)
> plot(nb7rt, xy)
> nb7rt <- cell2nb(7, 7, torus=TRUE)
> summary(nb7rt)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 196 
Percentage nonzero weights: 8.163265 
Average number of links: 4 
Link number distribution:

 4 
49 
49 least connected regions:
1:1 2:1 3:1 4:1 5:1 6:1 7:1 1:2 2:2 3:2 4:2 5:2 6:2 7:2 1:3 2:3 3:3 4:3 5:3 6:3 7:3 1:4 2:4 3:4 4:4 5:4 6:4 7:4 1:5 2:5 3:5 4:5 5:5 6:5 7:5 1:6 2:6 3:6 4:6 5:6 6:6 7:6 1:7 2:7 3:7 4:7 5:7 6:7 7:7 with 4 links
49 most connected regions:
1:1 2:1 3:1 4:1 5:1 6:1 7:1 1:2 2:2 3:2 4:2 5:2 6:2 7:2 1:3 2:3 3:3 4:3 5:3 6:3 7:3 1:4 2:4 3:4 4:4 5:4 6:4 7:4 1:5 2:5 3:5 4:5 5:5 6:5 7:5 1:6 2:6 3:6 4:6 5:6 6:6 7:6 1:7 2:7 3:7 4:7 5:7 6:7 7:7 with 4 links
> 
> 
> 
> cleanEx(); ..nameEx <- "choynowski"
> 
> ### * choynowski
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: choynowski
> ### Title: Choynowski probability map values
> ### Aliases: choynowski
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(auckland)
> res <- choynowski(auckland$Deaths.1977.85, 9*auckland$Under.5.1981)
> res1 <- probmap(auckland$Deaths.1977.85, 9*auckland$Under.5.1981)
> table(abs(res$pmap - res1$pmap) < 0.00001, res$type)
       
        FALSE TRUE
  FALSE    74    0
  TRUE      0   93
> plot(auckpolys, forcefill=FALSE)
> lt005 <- (res$pmap < 0.05) & (res$type)
> ge005 <- (res$pmap < 0.05) & (!res$type)
> plot(subset(auckpolys, lt005), add=TRUE, col=grey(2/7), forcefill=FALSE) 
> plot(subset(auckpolys, ge005), add=TRUE, col=grey(5/7), forcefill=FALSE)
> legend(c(70,90), c(70,95), fill=grey(c(2,5)/7),
+  legend=c("low", "high"), bty="n")
> 
> 
> 
> cleanEx(); ..nameEx <- "columbus"
> 
> ### * columbus
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: columbus
> ### Title: Columbus OH spatial analysis data set
> ### Aliases: columbus col.gal.nb coords polys bbs
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(columbus)
> summary(columbus)
      AREA           PERIMETER        COLUMBUS.    COLUMBUS.I     POLYID  
 Min.   :0.03438   Min.   :0.9021   Min.   : 2   Min.   : 1   Min.   : 1  
 1st Qu.:0.09315   1st Qu.:1.4023   1st Qu.:14   1st Qu.:13   1st Qu.:13  
 Median :0.17477   Median :1.8410   Median :26   Median :25   Median :25  
 Mean   :0.18649   Mean   :1.8887   Mean   :26   Mean   :25   Mean   :25  
 3rd Qu.:0.24669   3rd Qu.:2.1992   3rd Qu.:38   3rd Qu.:37   3rd Qu.:37  
 Max.   :0.69926   Max.   :5.0775   Max.   :50   Max.   :49   Max.   :49  
      NEIG        HOVAL            INC             CRIME        
 Min.   : 1   Min.   :17.90   Min.   : 4.477   Min.   : 0.1783  
 1st Qu.:13   1st Qu.:25.70   1st Qu.: 9.963   1st Qu.:20.0485  
 Median :25   Median :33.50   Median :13.380   Median :34.0008  
 Mean   :25   Mean   :38.44   Mean   :14.375   Mean   :35.1288  
 3rd Qu.:37   3rd Qu.:43.30   3rd Qu.:18.324   3rd Qu.:48.5855  
 Max.   :49   Max.   :96.40   Max.   :31.070   Max.   :68.8920  
      OPEN             PLUMB             DISCBD            X        
 Min.   : 0.0000   Min.   : 0.1327   Min.   :0.370   Min.   :24.25  
 1st Qu.: 0.2598   1st Qu.: 0.3323   1st Qu.:1.700   1st Qu.:36.15  
 Median : 1.0061   Median : 1.0239   Median :2.670   Median :39.61  
 Mean   : 2.7709   Mean   : 2.3639   Mean   :2.852   Mean   :39.46  
 3rd Qu.: 3.9364   3rd Qu.: 2.5343   3rd Qu.:3.890   3rd Qu.:43.44  
 Max.   :24.9981   Max.   :18.8111   Max.   :5.570   Max.   :51.24  
       Y              AREA             NSA              NSB        
 Min.   :24.96   Min.   : 1.093   Min.   :0.0000   Min.   :0.0000  
 1st Qu.:28.26   1st Qu.: 3.193   1st Qu.:0.0000   1st Qu.:0.0000  
 Median :31.91   Median : 6.029   Median :0.0000   Median :1.0000  
 Mean   :32.37   Mean   : 6.372   Mean   :0.4898   Mean   :0.5102  
 3rd Qu.:35.92   3rd Qu.: 7.989   3rd Qu.:1.0000   3rd Qu.:1.0000  
 Max.   :44.07   Max.   :21.282   Max.   :1.0000   Max.   :1.0000  
       EW               CP             THOUS          NEIGNO    
 Min.   :0.0000   Min.   :0.0000   Min.   :1000   Min.   :1001  
 1st Qu.:0.0000   1st Qu.:0.0000   1st Qu.:1000   1st Qu.:1013  
 Median :1.0000   Median :0.0000   Median :1000   Median :1025  
 Mean   :0.5918   Mean   :0.4898   Mean   :1000   Mean   :1025  
 3rd Qu.:1.0000   3rd Qu.:1.0000   3rd Qu.:1000   3rd Qu.:1037  
 Max.   :1.0000   Max.   :1.0000   Max.   :1000   Max.   :1049  
     PERIM       
 Min.   :0.9021  
 1st Qu.:1.4023  
 Median :1.8410  
 Mean   :1.8887  
 3rd Qu.:2.1992  
 Max.   :5.0775  
> 
> 
> 
> cleanEx(); ..nameEx <- "compon"
> 
> ### * compon
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: Graph Components
> ### Title: Depth First Search on Neighbor Lists
> ### Aliases: n.comp.nb
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> plot(col.gal.nb, coords, col="grey")
> col2 <- droplinks(col.gal.nb, 21)
> plot(col2, coords, add=TRUE)
> res <- n.comp.nb(col2)
> table(res$comp.id)

 1  2  3 
42  1  6 
> points(coords, col=res$comp.id, pch=16)
> 
> 
> 
> cleanEx(); ..nameEx <- "diffnb"
> 
> ### * diffnb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: diffnb
> ### Title: Differences between neighbours lists
> ### Aliases: diffnb
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> knn1 <- knearneigh(coords, 1)
> knn2 <- knearneigh(coords, 2)
> nb1 <- knn2nb(knn1, row.names=rownames(columbus))
> nb2 <- knn2nb(knn2, row.names=rownames(columbus))
> diffs <- diffnb(nb2, nb1)
Neighbour difference for region id: 1005 in relation to id: 1001 
Neighbour difference for region id: 1001 in relation to id: 1005 
Neighbour difference for region id: 1006 in relation to id: 1002 
Neighbour difference for region id: 1002 in relation to id: 1001 
Neighbour difference for region id: 1007 in relation to id: 1003 
Neighbour difference for region id: 1008 in relation to id: 1007 
Neighbour difference for region id: 1004 in relation to id: 1003 
Neighbour difference for region id: 1003 in relation to id: 1004 
Neighbour difference for region id: 1018 in relation to id: 1008 
Neighbour difference for region id: 1010 in relation to id: 1018 
Neighbour difference for region id: 1038 in relation to id: 1039 
Neighbour difference for region id: 1037 in relation to id: 1039 
Neighbour difference for region id: 1039 in relation to id: 1037 
Neighbour difference for region id: 1040 in relation to id: 1041 
Neighbour difference for region id: 1009 in relation to id: 1032 
Neighbour difference for region id: 1036 in relation to id: 1009 
Neighbour difference for region id: 1011 in relation to id: 1010 
Neighbour difference for region id: 1042 in relation to id: 1041 
Neighbour difference for region id: 1041 in relation to id: 1042 
Neighbour difference for region id: 1017 in relation to id: 1012 
Neighbour difference for region id: 1043 in relation to id: 1044 
Neighbour difference for region id: 1019 in relation to id: 1020 
Neighbour difference for region id: 1012 in relation to id: 1013 
Neighbour difference for region id: 1035 in relation to id: 1041 
Neighbour difference for region id: 1032 in relation to id: 1009 
Neighbour difference for region id: 1020 in relation to id: 1019 
Neighbour difference for region id: 1021 in relation to id: 1019 
Neighbour difference for region id: 1031 in relation to id: 1024 
Neighbour difference for region id: 1033 in relation to id: 1031 
Neighbour difference for region id: 1034 in relation to id: 1030 
Neighbour difference for region id: 1045 in relation to id: 1044 
Neighbour difference for region id: 1013 in relation to id: 1016 
Neighbour difference for region id: 1022 in relation to id: 1023 
Neighbour difference for region id: 1044 in relation to id: 1045 
Neighbour difference for region id: 1023 in relation to id: 1025 
Neighbour difference for region id: 1046 in relation to id: 1049 
Neighbour difference for region id: 1030 in relation to id: 1029 
Neighbour difference for region id: 1024 in relation to id: 1030 
Neighbour difference for region id: 1047 in relation to id: 1046 
Neighbour difference for region id: 1016 in relation to id: 1014 
Neighbour difference for region id: 1014 in relation to id: 1016 
Neighbour difference for region id: 1049 in relation to id: 1046 
Neighbour difference for region id: 1029 in relation to id: 1027 
Neighbour difference for region id: 1025 in relation to id: 1026 
Neighbour difference for region id: 1028 in relation to id: 1029 
Neighbour difference for region id: 1048 in relation to id: 1046 
Neighbour difference for region id: 1015 in relation to id: 1016 
Neighbour difference for region id: 1027 in relation to id: 1026 
Neighbour difference for region id: 1026 in relation to id: 1025 
> library(maptools)
> plot(polys, border="grey", forcefill=FALSE)
> plot(nb1, coords, add=TRUE)
> plot(diffs, coords, add=TRUE, col="red", lty=2)
> title(main="Plot of first (black) and second (red)\nnearest neighbours")
> 
> 
> 
> cleanEx(); ..nameEx <- "dnearneigh"
> 
> ### * dnearneigh
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: dnearneigh
> ### Title: Neighbourhood contiguity by distance
> ### Aliases: dnearneigh
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> k1 <- knn2nb(knearneigh(coords))
> all.linked <- max(unlist(nbdists(k1, coords)))
> col.nb.0.all <- dnearneigh(coords, 0, all.linked, row.names=rownames(columbus))
> summary(col.nb.0.all, coords)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 252 
Percentage nonzero weights: 10.49563 
Average number of links: 5.142857 
Link number distribution:

 1  2  3  4  5  6  7  8  9 10 11 
 4  8  6  2  5  8  6  2  6  1  1 
4 least connected regions:
1008 1010 1043 1015 with 1 link
1 most connected region:
1031 with 11 links
Summary of link distances:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.1276  0.3608  0.4566  0.4331  0.5224  0.6189 

  The decimal point is 2 digit(s) to the left of the |

  12 | 88
  14 | 44
  16 | 
  18 | 7788
  20 | 0033
  22 | 772277
  24 | 4488
  26 | 8822
  28 | 2244
  30 | 00334466
  32 | 11114444001188
  34 | 0033446633
  36 | 1133559900335588
  38 | 1133668899003355
  40 | 44557777222266
  42 | 990022333399
  44 | 3322777799
  46 | 22223344666677001111225588
  48 | 00000011222299
  50 | 1122888800557799
  52 | 22223333446600
  54 | 00333377001133556677
  56 | 111133446666
  58 | 0022337799
  60 | 2299111199

> library(maptools)
> plot(polys, border="grey", forcefill=FALSE)
> plot(col.nb.0.all, coords, add=TRUE)
> title(main=paste("Distance based neighbours 0-",  format(all.linked),
+  " distance units", sep=""))
> data(state)
> us48.fipsno <- read.geoda(system.file("etc/weights/us48.txt",
+  package="spdep")[1])
> if (as.numeric(paste(version$major, version$minor, sep="")) < 19) {
+  m50.48 <- match(us48.fipsno$"State.name", state.name)
+ } else {
+  m50.48 <- match(us48.fipsno$"State_name", state.name)
+ }
> xy <- as.matrix(as.data.frame(state.center))[m50.48,]
> llk1 <- knn2nb(knearneigh(xy, k=1, lonlat=FALSE))
> all.linked <- max(unlist(nbdists(llk1, xy, lonlat=FALSE)))
> ll.nb <- dnearneigh(xy, 0, all.linked, lonlat=FALSE)
> summary(ll.nb, xy, lonlat=TRUE, scale=0.5)
Neighbour list object:
Number of regions: 48 
Number of nonzero links: 190 
Percentage nonzero weights: 8.246528 
Average number of links: 3.958333 
Link number distribution:

 1  2  3  4  5  7  8  9 10 
11  9  4  8  4  4  4  3  1 
11 least connected regions:
2 4 8 10 24 26 29 32 35 41 45 with 1 link
1 most connected region:
28 with 10 links
Summary of link distances:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  93.59  293.00  360.10  354.00  448.00  542.40 

  The decimal point is 2 digit(s) to the right of the |

  0 | 99
  1 | 00112233
  1 | 666699
  2 | 00112222334444444444
  2 | 667788999999
  3 | 000000001111111122222222222233333333334444
  3 | 555566666677777788888899999999
  4 | 0000001111223344
  4 | 555555555555666666777788888888889999
  5 | 000000111122334444

> gck1 <- knn2nb(knearneigh(xy, k=1, lonlat=TRUE))
> all.linked <- max(unlist(nbdists(gck1, xy, lonlat=TRUE)))
> gc.nb <- dnearneigh(xy, 0, all.linked, lonlat=TRUE)
> summary(gc.nb, xy, lonlat=TRUE, scale=0.5)
Neighbour list object:
Number of regions: 48 
Number of nonzero links: 219 
Percentage nonzero weights: 9.505208 
Average number of links: 4.5625 
Non-symmetric neighbours list
Link number distribution:

 1  2  3  4  5  6  7  8  9 10 
 6  8  6  8  5  2  3  3  5  2 
6 least connected regions:
2 4 8 29 41 45 with 1 link
2 most connected regions:
7 28 with 10 links
Summary of link distances:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  93.59  304.10  378.20  371.10  467.20  523.60 

  The decimal point is 2 digit(s) to the right of the |

  0 | 99
  1 | 00112233
  1 | 666699
  2 | 00112222334444444444
  2 | 667788999999
  3 | 000000001111111122222222222233333333334444
  3 | 555566666677777788888899999999
  4 | 00000011112233334444
  4 | 55555555555566666666667777888888888888999999
  5 | 00000000000000111111112222222222222

> plot(ll.nb, xy)
> plot(diffnb(ll.nb, gc.nb), xy, add=TRUE, col="red", lty=2)
Neighbour difference for region id: 2 in relation to id: 29 42 
Neighbour difference for region id: 5 in relation to id: 42 
Neighbour difference for region id: 7 in relation to id: 46 
Neighbour difference for region id: 10 in relation to id: 24 35 42 
Neighbour difference for region id: 11 in relation to id: 15 20 
Neighbour difference for region id: 12 in relation to id: 46 
Neighbour difference for region id: 13 in relation to id: 25 
Neighbour difference for region id: 14 in relation to id: 23 
Neighbour difference for region id: 15 in relation to id: 11 
Neighbour difference for region id: 18 in relation to id: 33 
Neighbour difference for region id: 19 in relation to id: 36 
Neighbour difference for region id: 20 in relation to id: 11 47 
Neighbour difference for region id: 21 in relation to id: 32 39 
Neighbour difference for region id: 23 in relation to id: 14 34 
Neighbour difference for region id: 24 in relation to id: 10 
Neighbour difference for region id: 25 in relation to id: 13 
Neighbour difference for region id: 26 in relation to id: 42 
Neighbour difference for region id: 32 in relation to id: 21 
Neighbour difference for region id: 33 in relation to id: 18 36 
Neighbour difference for region id: 34 in relation to id: 23 
Neighbour difference for region id: 35 in relation to id: 10 
Neighbour difference for region id: 36 in relation to id: 19 33 
Neighbour difference for region id: 38 in relation to id: 46 
Neighbour difference for region id: 39 in relation to id: 21 
Neighbour difference for region id: 42 in relation to id: 2 5 10 26 
Neighbour difference for region id: 46 in relation to id: 7 12 38 
Neighbour difference for region id: 47 in relation to id: 20 
> title(main="Differences between Euclidean and Great Circle neighbours")
> 
> 
> 
> cleanEx(); ..nameEx <- "droplinks"
> 
> ### * droplinks
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: droplinks
> ### Title: Drop links in a neighbours list
> ### Aliases: droplinks
> ### Keywords: spatial
> 
> ### ** Examples
> 
> rho <- c(0.2, 0.5, 0.95, 0.999, 1.0)
> ns <- c(5, 7, 9, 11, 13, 15, 17, 19)
> mns <- matrix(0, nrow=length(ns), ncol=length(rho))
> rownames(mns) <- ns
> colnames(mns) <- rho
> mxs <- matrix(0, nrow=length(ns), ncol=length(rho))
> rownames(mxs) <- ns
> colnames(mxs) <- rho
> for (i in 1:length(ns)) {
+   nblist <- cell2nb(ns[i], ns[i])
+   nbdropped <- droplinks(nblist, ((ns[i]*ns[i])+1)/2, sym=FALSE)
+   listw <- nb2listw(nbdropped, style="W", zero.policy=TRUE)
+   wmat <- listw2mat(listw)
+   for (j in 1:length(rho)) {
+     mat <- diag(ns[i]*ns[i]) - rho[j] * wmat
+     res <- diag(solve(t(mat) %*% mat))
+     mns[i,j] <- mean(res)
+     mxs[i,j] <- max(res)
+   }
+ }
> print(mns)
        0.2      0.5      0.95     0.999          1
5  1.038271 1.312627  9.486051  30.81487   32.04915
7  1.036443 1.295621 10.899580  83.25437   92.09812
9  1.035356 1.285145 10.798611 160.90951  195.02166
11 1.034639 1.278279 10.383083 254.83998  347.71145
13 1.034132 1.273442  9.968389 353.66366  555.88699
15 1.033753 1.269852  9.619387 447.19245  824.46560
17 1.033460 1.267082  9.337167 528.49015 1157.77630
19 1.033227 1.264879  9.109487 594.23907 1559.69614
> print(mxs)
        0.2      0.5     0.95     0.999          1
5  1.048834 1.401934 12.00215  39.22742   40.79967
7  1.048834 1.402174 14.66823 106.90031  118.01556
9  1.048834 1.402176 15.49606 207.28928  249.74893
11 1.048834 1.402176 15.75744 329.22973  443.97194
13 1.048834 1.402176 15.83957 458.75739  707.14827
15 1.048834 1.402176 15.86474 583.50722 1044.75562
17 1.048834 1.402176 15.87225 695.10288 1461.57017
19 1.048834 1.402176 15.87445 789.50575 1961.84025
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "eigenw"
> 
> ### * eigenw
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: eigenw
> ### Title: Spatial weights matrix eigenvalues
> ### Aliases: eigenw
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> W.eig <- eigenw(nb2listw(COL.nb, style="W"))
> 1/range(W.eig)
[1] -1.536177  1.000000
> S.eig <- eigenw(nb2listw(COL.nb, style="S"))
> 1/range(S.eig)
[1] -1.7364189  0.8918997
> B.eig <- eigenw(nb2listw(COL.nb, style="B"))
> 1/range(B.eig)
[1] -0.3229290  0.1692726
> 
> 
> 
> cleanEx(); ..nameEx <- "eire"
> 
> ### * eire
> 
> flush(stderr()); flush(stdout())
> 
> ### Encoding: latin1
> 
> ### Name: eire
> ### Title: Eire data sets
> ### Aliases: eire eire.df eire.polys.utm eire.coords.utm eire.nb
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(eire)
> summary(eire.df$A)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  23.92   27.92   29.26   29.53   30.94   35.86 
> brks <- round(fivenum(eire.df$A), digits=2)
> cols <- rev(heat.colors(4))
> library(maptools)
> plot(eire.polys.utm,
+  col=cols[findInterval(eire.df$A, brks)], forcefill=FALSE)
> title(main="Percentage with blood group A in Eire")
> legend(x=c(-50, 70), y=c(6120, 6050), leglabs(brks), fill=cols, bty="n")
> plot(eire.polys.utm, forcefill=FALSE)
> plot(eire.nb, eire.coords.utm, add=TRUE)
> lA <- lag.listw(nb2listw(eire.nb), eire.df$A)
> summary(lA)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  26.08   28.33   29.21   29.64   31.12   33.39 
> moran.test(spNamedVec("A", eire.df), nb2listw(eire.nb))

	Moran's I test under randomisation

data:  spNamedVec("A", eire.df)  
weights: nb2listw(eire.nb)  
 
Moran I statistic standard deviate = 4.6851, p-value = 1.399e-06
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
       0.55412382       -0.04000000        0.01608138 

> geary.test(spNamedVec("A", eire.df), nb2listw(eire.nb))

	Geary's C test under randomisation

data:  spNamedVec("A", eire.df) 
weights: nb2listw(eire.nb) 
 
Geary C statistic standard deviate = -4.5146, p-value = 3.172e-06
alternative hypothesis: less 
sample estimates:
Geary C statistic       Expectation          Variance 
       0.38011971        1.00000000        0.01885309 

> cor(lA, eire.df$A)
[1] 0.8144345
> moran.plot(spNamedVec("A", eire.df), nb2listw(eire.nb),
+  labels=rownames(eire.df))
Potentially influential observations of
	 lm(formula = wx ~ x) :

         dfb.1_ dfb.x dffit   cov.r   cook.d hat  
Carlow   -0.04   0.04  0.05    1.27_*  0.00   0.14
Cork      0.97  -0.93  1.04_*  0.92    0.47   0.19
Limerick -0.26   0.21 -0.52    0.74_*  0.11   0.05
Wexford   0.05  -0.06 -0.06    1.41_*  0.00   0.23
Wicklow  -0.19   0.19  0.22    1.35_*  0.02   0.21
> A.lm <- lm(A ~ towns + pale, data=eire.df)
> summary(A.lm)

Call:
lm(formula = A ~ towns + pale, data = eire.df)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.6420 -1.0340 -0.3428  1.0263  4.0460 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  27.5728     0.5448  50.614  < 2e-16 ***
towns        -0.3595     2.9672  -0.121 0.904610    
pale          4.3419     1.0851   4.001 0.000561 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 2.018 on 23 degrees of freedom
Multiple R-Squared: 0.5551,	Adjusted R-squared: 0.5164 
F-statistic: 14.35 on 2 and 23 DF,  p-value: 9.014e-05 

> res <- residuals(A.lm)
> brks <- c(min(res),-2,-1,0,1,2,max(res))
> cols <- rev(cm.colors(6))
> plot(eire.polys.utm, col=cols[findInterval(res, brks)], forcefill=FALSE)
> title(main="Regression residuals")
> legend(x=c(-50, 70), y=c(6120, 6050), legend=leglabs(brks), fill=cols,
+   bty="n")
> lm.morantest(A.lm, nb2listw(eire.nb))

	Global Moran's I for regression residuals

data:  
model: lm(formula = A ~ towns + pale, data = eire.df)
weights: nb2listw(eire.nb)
 
Moran I statistic standard deviate = 1.8003, p-value = 0.03591
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
        0.15085317        -0.06845969         0.01484007 

> lm.morantest.sad(A.lm, nb2listw(eire.nb))

	Saddlepoint approximation for global Moran's I (Barndorff-Nielsen
	formula)

data:  
model:lm(formula = A ~ towns + pale, data = eire.df)
weights: nb2listw(eire.nb)
 
Saddlepoint approximation = 1.7284, p-value = 0.04196
alternative hypothesis: greater 
sample estimates:
Observed Moran's I 
         0.1508532 

> lm.LMtests(A.lm, nb2listw(eire.nb), test="LMerr")

	Lagrange multiplier diagnostics for spatial dependence

data:  
model: lm(formula = A ~ towns + pale, data = eire.df)
weights: nb2listw(eire.nb)
 
LMerr = 1.1634, df = 1, p-value = 0.2808

> brks <- round(fivenum(eire.df$OWNCONS), digits=2)
> cols <- grey(4:1/5)
> plot(eire.polys.utm,
+  col=cols[findInterval(eire.df$OWNCONS, brks)], forcefill=FALSE)
> title(main="Percentage own consumption of agricultural produce")
> legend(x=c(-50, 70), y=c(6120, 6050), legend=leglabs(brks),
+   fill=cols, bty="n")
> moran.plot(spNamedVec("OWNCONS", eire.df), nb2listw(eire.nb))
Potentially influential observations of
	 lm(formula = wx ~ x) :

        dfb.1_ dfb.x dffit   cov.r   cook.d hat    
Donegal -0.02   0.03  0.04    1.33_*  0.00   0.18  
Kerry   -0.04  -0.21 -0.62    0.62_*  0.15   0.04  
Mayo     0.59  -0.79 -0.85    1.23    0.35   0.26_*
Sligo   -0.43   0.77  1.02_*  0.56_*  0.37   0.09  
> moran.test(spNamedVec("OWNCONS", eire.df), nb2listw(eire.nb))

	Moran's I test under randomisation

data:  spNamedVec("OWNCONS", eire.df)  
weights: nb2listw(eire.nb)  
 
Moran I statistic standard deviate = 5.8637, p-value = 2.263e-09
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
       0.71281837       -0.04000000        0.01648309 

> e.lm <- lm(OWNCONS ~ ROADACC, data=eire.df)
> res <- residuals(e.lm)
> brks <- c(min(res),-2,-1,0,1,2,max(res))
> cols <- rev(cm.colors(6))
> plot(eire.polys.utm, col=cols[findInterval(res, brks)], forcefill=FALSE)
> title(main="Regression residuals")
> legend(x=c(-50, 70), y=c(6120, 6050), legend=leglabs(brks), fill=cm.colors(6),
+   bty="n")
> lm.morantest(e.lm, nb2listw(eire.nb))

	Global Moran's I for regression residuals

data:  
model: lm(formula = OWNCONS ~ ROADACC, data = eire.df)
weights: nb2listw(eire.nb)
 
Moran I statistic standard deviate = 3.2575, p-value = 0.0005619
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
        0.33660565        -0.05877741         0.01473183 

> lm.morantest.sad(e.lm, nb2listw(eire.nb))

	Saddlepoint approximation for global Moran's I (Barndorff-Nielsen
	formula)

data:  
model:lm(formula = OWNCONS ~ ROADACC, data = eire.df)
weights: nb2listw(eire.nb)
 
Saddlepoint approximation = 2.9395, p-value = 0.001644
alternative hypothesis: greater 
sample estimates:
Observed Moran's I 
         0.3366057 

> lm.LMtests(e.lm, nb2listw(eire.nb), test="LMerr")

	Lagrange multiplier diagnostics for spatial dependence

data:  
model: lm(formula = OWNCONS ~ ROADACC, data = eire.df)
weights: nb2listw(eire.nb)
 
LMerr = 5.7925, df = 1, p-value = 0.01609

> print(localmoran.sad(e.lm, eire.nb, select=1:nrow(eire.df)))
             Local Morans I Saddlepoint    Pr. (Sad)
1 Carlow        0.216996683  0.95074844 1.708660e-01
2 Cavan        -0.372573613 -1.00603119 8.427997e-01
3 Clare         0.231975105  0.67166518 2.508984e-01
4 Cork          0.781935479  1.74761575 4.026529e-02
5 Donegal      -1.690640590 -1.72031078 9.573120e-01
6 Dublin       -0.160696921 -0.35212627 6.376282e-01
7 Galway        1.313714727  2.66849536 3.809592e-03
8 Kerry         0.365348659  0.78073279 2.174798e-01
9 Kildare      -0.025575445  0.04167665 4.833782e-01
10 Kilkenny     0.576843308  1.70897697 4.372761e-02
11 Laoghis     -0.059517978 -0.12155465 5.483741e-01
12 Leitrim      0.384845866  1.47227033 7.047395e-02
13 Limerick     0.118179867  0.45727712 3.237359e-01
14 Longford     1.416432004  2.51113769 6.017137e-03
15 Louth        0.562429203  1.07441571 1.413182e-01
16 Mayo         0.875727038  2.05251226 2.005995e-02
17 Meath        0.003678560  0.12813539 4.490209e-01
18 Monaghan     0.550983111  1.23999193 1.074892e-01
19 Offaly       0.151555560  0.80786519 2.095841e-01
20 Roscommon    2.043688390  4.53187292 2.923151e-06
21 Sligo       -0.475798710 -0.94578114 8.278699e-01
22 Tipperary   -0.034541063 -0.06919691 5.275836e-01
23 Waterford    0.857234228  1.91385108 2.781959e-02
24 Westmeath    0.451385718  1.36017204 8.688774e-02
25 Wexford      0.643718339  1.63188492 5.135187e-02
26 Wicklow      0.024419502  0.21197000 4.160652e-01
> 
> 
> 
> cleanEx(); ..nameEx <- "errorsarlm"
> 
> ### * errorsarlm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: errorsarlm
> ### Title: Spatial simultaneous autoregressive error model estimation
> ### Aliases: errorsarlm
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb, style="W"), method="eigen", quiet=FALSE)

Spatial autoregressive error model
 Jacobian calculated using neighbourhood matrix eigenvalues
Computing eigenvalues ...

(eigen) lambda:	 -0.5674437 	function value:	 -195.8051 
(eigen) lambda:	 0.03126655 	function value:	 -187.0219 
(eigen) lambda:	 0.4012898 	function value:	 -183.8422 
(eigen) lambda:	 0.6299767 	function value:	 -183.4895 
(eigen) lambda:	 0.5811116 	function value:	 -183.3887 
(eigen) lambda:	 0.554104 	function value:	 -183.3817 
(eigen) lambda:	 0.5621834 	function value:	 -183.3805 
(eigen) lambda:	 0.5617028 	function value:	 -183.3805 
(eigen) lambda:	 0.5617888 	function value:	 -183.3805 
(eigen) lambda:	 0.5617902 	function value:	 -183.3805 
(eigen) lambda:	 0.5617903 	function value:	 -183.3805 
(eigen) lambda:	 0.5617903 	function value:	 -183.3805 
> COL.errW.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb, style="W"), method="eigen", quiet=FALSE)

Spatial autoregressive error model
 Jacobian calculated using neighbourhood matrix eigenvalues
Computing eigenvalues ...

(eigen) lambda:	 -0.5674437 	function value:	 -195.8051 
(eigen) lambda:	 0.03126655 	function value:	 -187.0219 
(eigen) lambda:	 0.4012898 	function value:	 -183.8422 
(eigen) lambda:	 0.6299767 	function value:	 -183.4895 
(eigen) lambda:	 0.5811116 	function value:	 -183.3887 
(eigen) lambda:	 0.554104 	function value:	 -183.3817 
(eigen) lambda:	 0.5621834 	function value:	 -183.3805 
(eigen) lambda:	 0.5617028 	function value:	 -183.3805 
(eigen) lambda:	 0.5617888 	function value:	 -183.3805 
(eigen) lambda:	 0.5617902 	function value:	 -183.3805 
(eigen) lambda:	 0.5617903 	function value:	 -183.3805 
(eigen) lambda:	 0.5617903 	function value:	 -183.3805 
> COL.errB.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb, style="B"), method="eigen", quiet=FALSE)

Spatial autoregressive error model
 Jacobian calculated using neighbourhood matrix eigenvalues
Computing eigenvalues ...

(eigen) lambda:	 -0.1349247 	function value:	 -196.5231 
(eigen) lambda:	 -0.01873166 	function value:	 -188.4544 
(eigen) lambda:	 0.0530796 	function value:	 -184.5803 
(eigen) lambda:	 0.0974614 	function value:	 -182.6524 
(eigen) lambda:	 0.1248908 	function value:	 -182.0539 
(eigen) lambda:	 0.1474059 	function value:	 -182.6008 
(eigen) lambda:	 0.1229929 	function value:	 -182.0642 
(eigen) lambda:	 0.1261661 	function value:	 -182.0507 
(eigen) lambda:	 0.1269409 	function value:	 -182.0502 
(eigen) lambda:	 0.126872 	function value:	 -182.0502 
(eigen) lambda:	 0.1268641 	function value:	 -182.0502 
(eigen) lambda:	 0.1268645 	function value:	 -182.0502 
(eigen) lambda:	 0.1268645 	function value:	 -182.0502 
(eigen) lambda:	 0.1268645 	function value:	 -182.0502 
(eigen) lambda:	 0.1268645 	function value:	 -182.0502 
> COL.errW.SM <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb, style="W"), method="SparseM", quiet=FALSE)

Spatial autoregressive error model
 Jacobian calculated using sparse matrix techniques using SparseM
(SparseM) lambda:	 -0.2364499 	function value:	 -190.4287 
(SparseM) lambda:	 0.2354499 	function value:	 -185.0024 
(SparseM) lambda:	 0.5271001 	function value:	 -183.4053 
(SparseM) lambda:	 0.728364 	function value:	 -184.1244 
(SparseM) lambda:	 0.5304163 	function value:	 -183.4009 
(SparseM) lambda:	 0.5557478 	function value:	 -183.3812 
(SparseM) lambda:	 0.6216813 	function value:	 -183.4637 
(SparseM) lambda:	 0.562713 	function value:	 -183.3805 
(SparseM) lambda:	 0.5618852 	function value:	 -183.3805 
(SparseM) lambda:	 0.5617866 	function value:	 -183.3805 
(SparseM) lambda:	 0.5617903 	function value:	 -183.3805 
(SparseM) lambda:	 0.5617903 	function value:	 -183.3805 
(SparseM) lambda:	 0.5617903 	function value:	 -183.3805 
(SparseM) lambda:	 0.5617903 	function value:	 -183.3805 
> summary(COL.errW.eig, correlation=TRUE)

Call:
errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb, 
    style = "W"), method = "eigen", quiet = FALSE)

Residuals:
      Min        1Q    Median        3Q       Max 
-34.81174  -6.44031  -0.72142   7.61476  23.33626 

Type: error 
Coefficients: (asymptotic standard errors) 
             Estimate Std. Error z value  Pr(>|z|)
(Intercept) 59.893219   5.366163 11.1613 < 2.2e-16
INC         -0.941312   0.330569 -2.8476 0.0044057
HOVAL       -0.302250   0.090476 -3.3407 0.0008358

Lambda: 0.56179 LR test value: 7.9935 p-value: 0.0046945 
Asymptotic standard error: 0.13387 z-value: 4.1966 p-value: 2.7098e-05 
Wald statistic: 17.611 p-value: 2.7098e-05 

Log likelihood: -183.3805 for error model
ML residual variance (sigma squared): 95.575, (sigma: 9.7762)
Number of observations: 49 
Number of parameters estimated: 5 
AIC: 376.76, (AIC for lm: 382.75)

Correlation of Coefficients:
            sigma lambda (Intercept) INC  
lambda      -0.24                         
(Intercept)  0.00  0.00                   
INC          0.00  0.00  -0.56            
HOVAL        0.00  0.00  -0.26       -0.45

> summary(COL.errB.eig, correlation=TRUE)

Call:
errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb, 
    style = "B"), method = "eigen", quiet = FALSE)

Residuals:
      Min        1Q    Median        3Q       Max 
-32.19010  -5.22646  -0.69952   7.92588  24.23511 

Type: error 
Coefficients: (asymptotic standard errors) 
             Estimate Std. Error z value  Pr(>|z|)
(Intercept) 55.383118   5.449775 10.1625 < 2.2e-16
INC         -0.936595   0.319355 -2.9328 0.0033596
HOVAL       -0.299857   0.088678 -3.3814 0.0007212

Lambda: 0.12686 LR test value: 10.654 p-value: 0.0010983 
Asymptotic standard error: 0.021745 z-value: 5.8342 p-value: 5.4044e-09 
Wald statistic: 34.038 p-value: 5.4044e-09 

Log likelihood: -182.0502 for error model
ML residual variance (sigma squared): 88.744, (sigma: 9.4204)
Number of observations: 49 
Number of parameters estimated: 5 
AIC: 374.1, (AIC for lm: 382.75)

Correlation of Coefficients:
            sigma lambda (Intercept) INC  
lambda      -0.24                         
(Intercept)  0.00  0.00                   
INC          0.00  0.00  -0.60            
HOVAL        0.00  0.00  -0.30       -0.42

> summary(COL.errW.SM, correlation=TRUE)

Call:
errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb, 
    style = "W"), method = "SparseM", quiet = FALSE)

Residuals:
      Min        1Q    Median        3Q       Max 
-34.81174  -6.44031  -0.72142   7.61476  23.33626 

Type: error 
Coefficients: (asymptotic standard errors) 
             Estimate Std. Error z value  Pr(>|z|)
(Intercept) 59.893219   5.366162 11.1613 < 2.2e-16
INC         -0.941312   0.330569 -2.8476 0.0044057
HOVAL       -0.302250   0.090476 -3.3407 0.0008358

Lambda: 0.56179 LR test value: 7.9935 p-value: 0.0046945 

Log likelihood: -183.3805 for error model
ML residual variance (sigma squared): 95.575, (sigma: 9.7762)
Number of observations: 49 
Number of parameters estimated: 5 
AIC: 376.76, (AIC for lm: 382.75)

> NA.COL.OLD <- COL.OLD
> NA.COL.OLD$CRIME[20:25] <- NA
> COL.err.NA <- errorsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,
+  nb2listw(COL.nb), na.action=na.exclude)
> COL.err.NA$na.action
1020 1021 1022 1023 1024 1025 
  20   21   22   23   24   25 
attr(,"class")
[1] "exclude"
> COL.err.NA

Call:
errorsarlm(formula = CRIME ~ INC + HOVAL, data = NA.COL.OLD, 
    listw = nb2listw(COL.nb), na.action = na.exclude)
Type: error 

Coefficients:
(Intercept)         INC       HOVAL      lambda 
 58.2460530  -0.8473028  -0.3024909   0.5748430 

Log likelihood: -161.8763 
> resid(COL.err.NA)
        1001         1002         1003         1004         1005         1006 
 -4.18270828 -11.44133862   0.31874929 -34.47163066   2.42244752  -4.32095075 
        1007         1008         1009         1010         1011         1012 
  8.66744162 -13.38669925  -1.92276576  17.85753941  -1.11484610  -2.30434795 
        1013         1014         1015         1016         1017         1018 
 -8.16935127  -5.80500232   0.14973712   5.93191452  -7.03028248   2.39112833 
        1019         1020         1021         1022         1023         1024 
 -8.95099917           NA           NA           NA           NA           NA 
        1025         1026         1027         1028         1029         1030 
          NA  -2.52940719  -9.60025400  -6.95635593  -0.43630587   5.98493684 
        1031         1032         1033         1034         1035         1036 
  6.25882674   7.75527043  10.83413248  23.23927265  -0.05594936   1.43808582 
        1037         1038         1039         1040         1041         1042 
  9.51995270  12.18295374   8.31031721  17.06834506   7.04418408   7.50088942 
        1043         1044         1045         1046         1047         1048 
 -7.78485972  -6.79207465  -7.94977553 -11.25362129  -5.68994642   5.04837380 
        1049 
  2.22497376 
> 
> 
> 
> cleanEx(); ..nameEx <- "geary"
> 
> ### * geary
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: geary
> ### Title: Compute Geary's C
> ### Aliases: geary
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> col.W <- nb2listw(COL.nb, style="W")
> str(geary(COL.OLD$CRIME, col.W, length(COL.nb), length(COL.nb)-1,
+  Szero(col.W)))
List of 2
 $ C: num 0.53
 $ K: num 2.23
> 
> 
> 
> cleanEx(); ..nameEx <- "geary.mc"
> 
> ### * geary.mc
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: geary.mc
> ### Title: Permutation test for Geary's C statistic
> ### Aliases: geary.mc
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> sim1 <- geary.mc(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb, style="W"),
+  nsim=99, alternative="less")
> sim1

	Monte-Carlo simulation of Geary's C

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(COL.nb, style = "W") 
number of simulations + 1: 100 
 
statistic = 0.5299, observed rank = 1, p-value = 0.01
alternative hypothesis: less 

> mean(sim1$res)
[1] 0.9899218
> var(sim1$res)
[1] 0.008075363
> summary(sim1$res)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.5299  0.9419  0.9904  0.9899  1.0450  1.1740 
> colold.lags <- nblag(COL.nb, 3)
> sim2 <- geary.mc(spNamedVec("CRIME", COL.OLD), nb2listw(colold.lags[[2]],
+  style="W"), nsim=99)
> sim2

	Monte-Carlo simulation of Geary's C

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(colold.lags[[2]], style = "W") 
number of simulations + 1: 100 
 
statistic = 0.8113, observed rank = 1, p-value = 0.01
alternative hypothesis: less 

> summary(sim2$res)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.8113  0.9398  1.0010  0.9954  1.0400  1.1530 
> sim3 <- geary.mc(spNamedVec("CRIME", COL.OLD), nb2listw(colold.lags[[3]],
+  style="W"), nsim=99)
> sim3

	Monte-Carlo simulation of Geary's C

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(colold.lags[[3]], style = "W") 
number of simulations + 1: 100 
 
statistic = 1.1303, observed rank = 96, p-value = 0.96
alternative hypothesis: less 

> summary(sim3$res)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.7883  0.9357  0.9938  0.9900  1.0340  1.1900 
> 
> 
> 
> cleanEx(); ..nameEx <- "geary.test"
> 
> ### * geary.test
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: geary.test
> ### Title: Geary's C test for spatial autocorrelation
> ### Aliases: geary.test
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> geary.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb, style="W"))

	Geary's C test under randomisation

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(COL.nb, style = "W") 
 
Geary C statistic standard deviate = -4.7605, p-value = 9.655e-07
alternative hypothesis: less 
sample estimates:
Geary C statistic       Expectation          Variance 
       0.52986993        1.00000000        0.00975278 

> geary.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb, style="W"),
+  randomisation=FALSE)

	Geary's C test under normality

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(COL.nb, style = "W") 
 
Geary C statistic standard deviate = -4.6388, p-value = 1.752e-06
alternative hypothesis: less 
sample estimates:
Geary C statistic       Expectation          Variance 
       0.52986993        1.00000000        0.01027137 

> colold.lags <- nblag(COL.nb, 3)
> geary.test(spNamedVec("CRIME", COL.OLD), nb2listw(colold.lags[[2]],
+  style="W"))

	Geary's C test under randomisation

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(colold.lags[[2]], style = "W") 
 
Geary C statistic standard deviate = -2.2896, p-value = 0.01102
alternative hypothesis: less 
sample estimates:
Geary C statistic       Expectation          Variance 
      0.811285136       1.000000000       0.006793327 

> geary.test(spNamedVec("CRIME", COL.OLD), nb2listw(colold.lags[[3]],
+  style="W"), alternative="greater")

	Geary's C test under randomisation

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(colold.lags[[3]], style = "W") 
 
Geary C statistic standard deviate = 1.5667, p-value = 0.05859
alternative hypothesis: greater 
sample estimates:
Geary C statistic       Expectation          Variance 
      1.130277918       1.000000000       0.006914551 

> print(is.symmetric.nb(COL.nb))
[1] TRUE
> COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4))
> print(is.symmetric.nb(COL.k4.nb))
Non-symmetric neighbours list
[1] FALSE
> geary.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.k4.nb, style="W"))

	Geary's C test under randomisation

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(COL.k4.nb, style = "W") 
 
Geary C statistic standard deviate = -12.3013, p-value < 2.2e-16
alternative hypothesis: less 
sample estimates:
Geary C statistic       Expectation          Variance 
      0.424057549       1.000000000       0.002192075 

> geary.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.k4.nb, style="W"),
+  randomisation=FALSE)
Warning in sqrt(VC) : NaNs produced

	Geary's C test under normality

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(COL.k4.nb, style = "W") 
 
Geary C statistic standard deviate = NaN, p-value = NA
alternative hypothesis: less 
sample estimates:
Geary C statistic       Expectation          Variance 
     0.4240575491      1.0000000000     -0.0008663057 

> cat("Note non-symmetric weights matrix - use listw2U()\n")
Note non-symmetric weights matrix - use listw2U()
> geary.test(spNamedVec("CRIME", COL.OLD), listw2U(nb2listw(COL.k4.nb,
+  style="W")))

	Geary's C test under randomisation

data:  spNamedVec("CRIME", COL.OLD) 
weights: listw2U(nb2listw(COL.k4.nb, style = "W")) 
 
Geary C statistic standard deviate = -6.1267, p-value = 4.486e-10
alternative hypothesis: less 
sample estimates:
Geary C statistic       Expectation          Variance 
       0.42405755        1.00000000        0.00883705 

> geary.test(spNamedVec("CRIME", COL.OLD), listw2U(nb2listw(COL.k4.nb,
+  style="W")), randomisation=FALSE)

	Geary's C test under normality

data:  spNamedVec("CRIME", COL.OLD) 
weights: listw2U(nb2listw(COL.k4.nb, style = "W")) 
 
Geary C statistic standard deviate = -5.995, p-value = 1.017e-09
alternative hypothesis: less 
sample estimates:
Geary C statistic       Expectation          Variance 
      0.424057549       1.000000000       0.009229488 

> 
> 
> 
> cleanEx(); ..nameEx <- "getisord"
> 
> ### * getisord
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: getisord
> ### Title: Getis-Ord remote sensing example data
> ### Aliases: getisord x y xyz
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(getisord)
> image(x, y, t(matrix(xyz$val, nrow=16, ncol=16, byrow=TRUE)), asp=1)
> text(xyz$x, xyz$y, xyz$val, cex=0.7)
> polygon(c(195,225,225,195), c(195,195,225,225), lwd=2)
> title(main="Getis-Ord 1996 remote sensing data")
> 
> 
> 
> cleanEx(); ..nameEx <- "globalG.test"
> 
> ### * globalG.test
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: globalG.test
> ### Title: test for spatial autocorrelation
> ### Aliases: globalG.test
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(nc.sids)
> sidsrate79 <- (1000*nc.sids$SID79)/nc.sids$BIR79
> names(sidsrate79) <- rownames(nc.sids)
> dists <- c(10, 20, 30, 33, 40, 50, 60, 70, 80, 90, 100)
> ndists <- length(dists)
> ZG <- numeric(length=ndists)
> milesxy <- cbind(nc.sids$east, nc.sids$north)
> for (i in 1:ndists) {
+   thisnb <- dnearneigh(milesxy, 0, dists[i], row.names=rownames(nc.sids))
+   thislw <- nb2listw(thisnb, style="B", zero.policy=TRUE)
+   ZG[i] <- globalG.test(sidsrate79, thislw, zero.policy=TRUE)$statistic
+ }
> cbind(dists, ZG)
      dists          ZG
 [1,]    10  0.81651489
 [2,]    20  0.27046614
 [3,]    30 -0.11849772
 [4,]    33  0.40157023
 [5,]    40 -0.04345713
 [6,]    50  0.58686472
 [7,]    60 -0.35823892
 [8,]    70 -0.27864299
 [9,]    80 -0.18791364
[10,]    90  0.11457610
[11,]   100  0.31591356
> 
> 
> 
> cleanEx(); ..nameEx <- "graphneigh"
> 
> ### * graphneigh
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: graphneigh
> ### Title: Graph based spatial weights
> ### Aliases: gabrielneigh relativeneigh soi.graph plot.Gabriel
> ###   plot.relative graph2nb
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> par(mfrow=c(2,2))
> col.tri.nb<-tri2nb(coords)
> col.gab.nb<-graph2nb(gabrielneigh(coords), sym=TRUE)
> col.rel.nb<- graph2nb(relativeneigh(coords), sym=TRUE)
> col.soi.nb<- graph2nb(soi.graph(col.tri.nb,coords), sym=TRUE)
> library(maptools)
> plot(polys, border="grey", forcefill=FALSE)
> plot(col.tri.nb,coords,add=TRUE)
> title(main="Delaunay Triangulation")
> plot(polys, border="grey", forcefill=FALSE)
> plot(col.gab.nb, coords, add=TRUE)
> title(main="Gabriel Graph")
> plot(polys, border="grey", forcefill=FALSE)
> plot(col.rel.nb, coords, add=TRUE)
> title(main="Relative Neighbor Graph")
> plot(polys, border="grey", forcefill=FALSE)
> plot(col.soi.nb, coords, add=TRUE)
> title(main="Sphere of Influence Graph")
> par(mfrow=c(1,1))
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "hopkins"
> 
> ### * hopkins
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: hopkins
> ### Title: Hopkins burnt savanna herb remains
> ### Aliases: hopkins
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(hopkins)
> image(1:32, 1:32, hopkins[5:36,36:5], breaks=c(-0.5, 3.5, 20),
+  col=c("white", "black"))
> box()
> 
> 
> 
> cleanEx(); ..nameEx <- "include.self"
> 
> ### * include.self
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: include.self
> ### Title: Include self in neighbours list
> ### Aliases: include.self
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> summary(col.gal.nb, coords)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 230 
Percentage nonzero weights: 9.579342 
Average number of links: 4.693878 
Link number distribution:

 2  3  4  5  6  7  8  9 10 
 7  7 13  4  9  6  1  1  1 
7 least connected regions:
1005 1008 1045 1047 1049 1048 1015 with 2 links
1 most connected region:
1017 with 10 links
Summary of link distances:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.1276  0.3613  0.4566  0.4694  0.5536  0.8924 

  The decimal point is 1 digit(s) to the left of the |

  1 | 3344
  1 | 99
  2 | 000011333344
  2 | 556677779999
  3 | 000011222222223344444444
  3 | 556666777777888888889999999999
  4 | 00001111112233333333334444
  4 | 55666666666666777777777788888899
  5 | 0011112222222222222233334444
  5 | 556666667788
  6 | 000000112244
  6 | 5577889999
  7 | 11112244
  7 | 557777
  8 | 1144
  8 | 55999999

> summary(include.self(col.gal.nb), coords)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 279 
Percentage nonzero weights: 11.62016 
Average number of links: 5.693878 
Link number distribution:

 3  4  5  6  7  8  9 10 11 
 7  7 13  4  9  6  1  1  1 
7 least connected regions:
1005 1008 1045 1047 1049 1048 1015 with 3 links
1 most connected region:
1017 with 11 links
Summary of link distances:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.0000  0.2576  0.4073  0.3870  0.5232  0.8924 

  The decimal point is 1 digit(s) to the left of the |

  0 | 0000000000000000000000000000000000000000000000000
  0 | 
  1 | 3344
  1 | 99
  2 | 000011333344
  2 | 556677779999
  3 | 000011222222223344444444
  3 | 556666777777888888889999999999
  4 | 00001111112233333333334444
  4 | 55666666666666777777777788888899
  5 | 0011112222222222222233334444
  5 | 556666667788
  6 | 000000112244
  6 | 5577889999
  7 | 11112244
  7 | 557777
  8 | 1144
  8 | 55999999

> 
> 
> 
> cleanEx(); ..nameEx <- "invIrM"
> 
> ### * invIrM
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: invIrM
> ### Title: Compute SAR generating operator
> ### Aliases: invIrM invIrW
> ### Keywords: spatial
> 
> ### ** Examples
> 
> 
> nb7rt <- cell2nb(7, 7, torus=TRUE)
> x <- matrix(rnorm(500*length(nb7rt)), nrow=length(nb7rt))
> res0 <- apply(invIrM(nb7rt, rho=0.0) %*% x, 2, function(x) var(x)/length(x))
> res2 <- apply(invIrM(nb7rt, rho=0.2) %*% x, 2, function(x) var(x)/length(x))
> res4 <- apply(invIrM(nb7rt, rho=0.4) %*% x, 2, function(x) var(x)/length(x))
> res6 <- apply(invIrM(nb7rt, rho=0.6) %*% x, 2, function(x) var(x)/length(x))
> res8 <- apply(invIrM(nb7rt, rho=0.8) %*% x, 2, function(x) var(x)/length(x))
> res9 <- apply(invIrM(nb7rt, rho=0.9) %*% x, 2, function(x) var(x)/length(x))
> plot(density(res9), col="red", xlim=c(-0.01, max(density(res9)$x)),
+   ylim=range(density(res0)$y),
+   xlab="estimated variance of the mean",
+   main=expression(paste("Effects of spatial autocorrelation for different ",
+     rho, " values")))
> lines(density(res0), col="black")
> lines(density(res2), col="brown")
> lines(density(res4), col="green")
> lines(density(res6), col="orange")
> lines(density(res8), col="pink")
> legend(c(-0.02, 0.01), c(7, 25), legend=c("0.0", "0.2", "0.4", "0.6", "0.8", "0.9"), col=c("black", "brown", "green", "orange", "pink", "red"), lty=1, bty="n")
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "joincount.mc"
> 
> ### * joincount.mc
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: joincount.mc
> ### Title: Permutation test for same colour join count statistics
> ### Aliases: joincount.mc
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
> names(HICRIME) <- rownames(COL.OLD)
> joincount.mc(HICRIME, nb2listw(COL.nb, style="B"), nsim=99)

	Monte-Carlo simulation of join-count statistic

data:  HICRIME 
weights: nb2listw(COL.nb, style = "B") 
number of simulations + 1: 100 
 
Join-count statistic for low = 34, rank of observed statistic = 86,
p-value = 0.14
alternative hypothesis: greater 
sample estimates:
    mean of simulation variance of simulation 
              29.01010               19.29582 


	Monte-Carlo simulation of join-count statistic

data:  HICRIME 
weights: nb2listw(COL.nb, style = "B") 
number of simulations + 1: 100 
 
Join-count statistic for high = 54, rank of observed statistic = 100,
p-value = 0.01
alternative hypothesis: greater 
sample estimates:
    mean of simulation variance of simulation 
              27.82828               18.06205 

> joincount.test(HICRIME, nb2listw(COL.nb, style="B"))

	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.nb, style = "B") 
 
Std. deviate for low = 1.0141, p-value = 0.1553
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
             34.00000              29.59184              18.89550 


	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.nb, style = "B") 
 
Std. deviate for high = 6.3307, p-value = 1.220e-10
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
             54.00000              27.22449              17.88838 

> 
> 
> 
> cleanEx(); ..nameEx <- "joincount.multi"
> 
> ### * joincount.multi
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: joincount.multi
> ### Title: BB, BW and Jtot join count statistic for k-coloured factors
> ### Aliases: joincount.multi print.jcmulti
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
> names(HICRIME) <- rownames(COL.OLD)
> joincount.multi(HICRIME, nb2listw(COL.nb, style="B"))
          Joincount Expected Variance z-value
low:low      34.000   29.592   18.895  1.0141
high:high    54.000   27.224   17.888  6.3307
high:low     28.000   59.184   26.233 -6.0884
Jtot         28.000   59.184   26.233 -6.0884
> data(hopkins)
> image(1:32, 1:32, hopkins[5:36,36:5], breaks=c(-0.5, 3.5, 20),
+  col=c("white", "black"))
> box()
> hopkins.rook.nb <- cell2nb(32, 32, type="rook")
> unlist(spweights.constants(nb2listw(hopkins.rook.nb, style="B")))
      n      n1      n2      n3      nn      S0      S1      S2 
   1024    1023    1022    1021 1048576    3968    7936   61984 
> hopkins.queen.nb <- cell2nb(32, 32, type="queen")
> hopkins.bishop.nb <- diffnb(hopkins.rook.nb, hopkins.queen.nb, verbose=FALSE)
> hopkins4 <- hopkins[5:36,36:5]
> hopkins4[which(hopkins4 > 3, arr.ind=TRUE)] <- 4
> hopkins4.f <- factor(hopkins4)
> table(hopkins4.f)
hopkins4.f
  0   1   2   3   4 
657 215  98  30  24 
> joincount.multi(hopkins4.f, nb2listw(hopkins.rook.nb, style="B"))
      Joincount   Expected   Variance z-value
0:0   864.00000  816.27273  116.05233  4.4304
1:1    94.00000   87.14015   55.25216  0.9229
2:2    18.00000   18.00379   14.81562 -0.0010
3:3     2.00000    1.64773    1.55539  0.2825
4:4     5.00000    1.04545    0.99845  3.9576
1:0   503.00000  535.05682  227.76750 -2.1241
2:0   213.00000  243.88636   97.21769 -3.1325
2:1    99.00000   79.81061   59.01930  2.4978
3:0    61.00000   74.65909   28.58592 -2.5547
3:1    28.00000   24.43182   18.99976  0.8186
3:2    15.00000   11.13636    9.82411  1.2327
4:0    40.00000   59.72727   22.78583 -4.1327
4:1    23.00000   19.54545   15.26564  0.8842
4:2    14.00000    8.90909    7.90051  1.8112
4:3     5.00000    2.72727    2.58616  1.4133
Jtot 1001.00000 1059.89015  273.78610 -3.5591
> cat("replicates Upton & Fingleton table 3.4 (p. 166)\n")
replicates Upton & Fingleton table 3.4 (p. 166)
> joincount.multi(hopkins4.f, nb2listw(hopkins.bishop.nb, style="B"))
      Joincount   Expected   Variance z-value
0:0   823.00000  790.76420  144.44877  2.6821
1:1   101.00000   84.41702   55.98143  2.2164
2:2    19.00000   17.44117   14.61542  0.4077
3:3     3.00000    1.59624    1.51444  1.1407
4:4     3.00000    1.01278    0.97111  2.0166
1:0   497.00000  518.33629  234.93545 -1.3920
2:0   216.00000  236.26491  104.42142 -1.9831
2:1    81.00000   77.31652   58.70829  0.4807
3:0    58.00000   72.32599   31.49151 -2.5529
3:1    21.00000   23.66832   18.85316 -0.6145
3:2    17.00000   10.78835    9.62487  2.0022
4:0    48.00000   57.86080   25.15973 -1.9659
4:1    21.00000   18.93466   15.14473  0.5307
4:2    10.00000    8.63068    7.73708  0.4923
4:3     4.00000    2.64205    2.51686  0.8560
Jtot  973.00000 1026.76858  284.51030 -3.1877
> cat("replicates Upton & Fingleton table 3.6 (p. 168)\n")
replicates Upton & Fingleton table 3.6 (p. 168)
> joincount.multi(hopkins4.f, nb2listw(hopkins.queen.nb, style="B"))
     Joincount  Expected  Variance z-value
0:0  1687.0000 1607.0369  303.8034  4.5877
1:1   195.0000  171.5572  114.2057  2.1936
2:2    37.0000   35.4450   29.6821  0.2854
3:3     5.0000    3.2440    3.0687  1.0024
4:4     8.0000    2.0582    1.9674  4.2361
1:0  1000.0000 1053.3931  480.6959 -2.4353
2:0   429.0000  480.1513  215.0360 -3.4882
2:1   180.0000  157.1271  119.3987  2.0932
3:0   119.0000  146.9851   65.1029 -3.4684
3:1    49.0000   48.1001   38.3268  0.1454
3:2    32.0000   21.9247   19.5237  2.2802
4:0    88.0000  117.5881   52.0312 -4.1019
4:1    44.0000   38.4801   30.7868  0.9948
4:2    24.0000   17.5398   15.6933  1.6308
4:3     9.0000    5.3693    5.0994  1.6078
Jtot 1974.0000 2086.6587  582.8326 -4.6665
> cat("replicates Upton & Fingleton table 3.7 (p. 169)\n")
replicates Upton & Fingleton table 3.7 (p. 169)
> 
> 
> 
> cleanEx(); ..nameEx <- "joincount.test"
> 
> ### * joincount.test
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: joincount.test
> ### Title: BB join count statistic for k-coloured factors
> ### Aliases: joincount.test print.jclist
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> HICRIME <- cut(COL.OLD$CRIME, breaks=c(0,35,80), labels=c("low","high"))
> names(HICRIME) <- rownames(COL.OLD)
> joincount.test(HICRIME, nb2listw(COL.nb, style="B"))

	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.nb, style = "B") 
 
Std. deviate for low = 1.0141, p-value = 0.1553
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
             34.00000              29.59184              18.89550 


	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.nb, style = "B") 
 
Std. deviate for high = 6.3307, p-value = 1.220e-10
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
             54.00000              27.22449              17.88838 

> joincount.test(HICRIME, nb2listw(COL.nb, style="C"))

	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.nb, style = "C") 
 
Std. deviate for low = 1.0141, p-value = 0.1553
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
             7.181034              6.250000              0.842897 


	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.nb, style = "C") 
 
Std. deviate for high = 6.3307, p-value = 1.220e-10
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
           11.4051724             5.7500000             0.7979712 

> joincount.test(HICRIME, nb2listw(COL.nb, style="S"))

	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.nb, style = "S") 
 
Std. deviate for low = 2.5786, p-value = 0.00496
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
            8.2425673             6.2500000             0.5971141 


	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.nb, style = "S") 
 
Std. deviate for high = 6.1736, p-value = 3.337e-10
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
           10.4249914             5.7500000             0.5734265 

> joincount.test(HICRIME, nb2listw(COL.nb, style="W"))

	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.nb, style = "W") 
 
Std. deviate for low = 4.6675, p-value = 1.524e-06
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
            9.5190476             6.2500000             0.4905378 


	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.nb, style = "W") 
 
Std. deviate for high = 5.1205, p-value = 1.523e-07
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
            9.2920635             5.7500000             0.4784979 

> by(card(COL.nb), HICRIME, summary)
INDICES: low
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   2.00    2.00    4.00    3.84    4.00   10.00 
------------------------------------------------------------ 
INDICES: high
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  3.000   4.750   6.000   5.667   7.000   9.000 
> print(is.symmetric.nb(COL.nb))
[1] TRUE
> COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4))
> print(is.symmetric.nb(COL.k4.nb))
Non-symmetric neighbours list
[1] FALSE
> joincount.test(HICRIME, nb2listw(COL.k4.nb, style="B"))
Warning in sqrt(Vjc[i]) : NaNs produced
Warning in sqrt(Vjc[i]) : NaNs produced

	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.k4.nb, style = "B") 
 
Std. deviate for low = NaN, p-value = NA
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
            36.500000             25.000000             -5.856492 


	Join count test under nonfree sampling

data:  HICRIME 
weights: nb2listw(COL.k4.nb, style = "B") 
 
Std. deviate for high = NaN, p-value = NA
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
             40.50000              23.00000              -4.97449 

> cat("Note non-symmetric weights matrix - use listw2U()\n")
Note non-symmetric weights matrix - use listw2U()
> joincount.test(HICRIME, listw2U(nb2listw(COL.k4.nb, style="B")))

	Join count test under nonfree sampling

data:  HICRIME 
weights: listw2U(nb2listw(COL.k4.nb, style = "B")) 
 
Std. deviate for low = 4.3698, p-value = 6.217e-06
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
            36.500000             25.000000              6.925749 


	Join count test under nonfree sampling

data:  HICRIME 
weights: listw2U(nb2listw(COL.k4.nb, style = "B")) 
 
Std. deviate for high = 6.7239, p-value = 8.845e-12
alternative hypothesis: greater 
sample estimates:
Same colour statistic           Expectation              Variance 
            40.500000             23.000000              6.773773 

> 
> 
> 
> cleanEx(); ..nameEx <- "knearneigh"
> 
> ### * knearneigh
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: knearneigh
> ### Title: K nearest neighbours for spatial weights
> ### Aliases: knearneigh
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> col.knn <- knearneigh(coords, k=4)
> library(maptools)
> plot(polys, border="grey", forcefill=FALSE)
> plot(knn2nb(col.knn), coords, add=TRUE)
> title(main="K nearest neighbours, k = 4")
> data(state)
> us48.fipsno <- read.geoda(system.file("etc/weights/us48.txt",
+  package="spdep")[1])
> if (as.numeric(paste(version$major, version$minor, sep="")) < 19) {
+  m50.48 <- match(us48.fipsno$"State.name", state.name)
+ } else {
+  m50.48 <- match(us48.fipsno$"State_name", state.name)
+ }
> xy <- as.matrix(as.data.frame(state.center))[m50.48,]
> llk4.nb <- knn2nb(knearneigh(xy, k=4, lonlat=FALSE))
> gck4.nb <- knn2nb(knearneigh(xy, k=4, lonlat=TRUE))
> plot(llk4.nb, xy)
> plot(diffnb(llk4.nb, gck4.nb), xy, add=TRUE, col="red", lty=2)
Neighbour difference for region id: 10 in relation to id: 26 48 
Neighbour difference for region id: 11 in relation to id: 15 47 
Neighbour difference for region id: 23 in relation to id: 14 34 
Neighbour difference for region id: 24 in relation to id: 5 32 42 45 
Neighbour difference for region id: 25 in relation to id: 5 32 
Neighbour difference for region id: 28 in relation to id: 30 36 
Neighbour difference for region id: 30 in relation to id: 19 27 28 36 
Neighbour difference for region id: 32 in relation to id: 24 48 
Neighbour difference for region id: 39 in relation to id: 13 14 
Neighbour difference for region id: 40 in relation to id: 9 12 
Neighbour difference for region id: 41 in relation to id: 14 29 
Neighbour difference for region id: 42 in relation to id: 5 48 
Neighbour difference for region id: 46 in relation to id: 15 18 31 36 
> title(main="Differences between Euclidean and Great Circle k=4 neighbours")
> summary(llk4.nb, xy, lonlat=TRUE)
Neighbour list object:
Number of regions: 48 
Number of nonzero links: 192 
Percentage nonzero weights: 8.333333 
Average number of links: 4 
Non-symmetric neighbours list
Link number distribution:

 4 
48 
48 least connected regions:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links
48 most connected regions:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links
Summary of link distances:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  93.59  297.60  393.50  414.50  513.00  955.90 

  The decimal point is 2 digit(s) to the right of the |

  0 | 99
  1 | 00112233
  1 | 666699
  2 | 00112222334444444444
  2 | 6677889999
  3 | 00000111112222222233333333334444
  3 | 556666777788899999
  4 | 0000001111233
  4 | 555555666666677788888899
  5 | 0000111111122222222344444
  5 | 55666679
  6 | 00233
  6 | 5667
  7 | 011234
  7 | 5889
  8 | 022
  8 | 79
  9 | 
  9 | 56

> summary(gck4.nb, xy, lonlat=TRUE)
Neighbour list object:
Number of regions: 48 
Number of nonzero links: 192 
Percentage nonzero weights: 8.333333 
Average number of links: 4 
Non-symmetric neighbours list
Link number distribution:

 4 
48 
48 least connected regions:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links
48 most connected regions:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 with 4 links
Summary of link distances:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  93.59  297.00  393.50  410.20  508.10  952.40 

  The decimal point is 2 digit(s) to the right of the |

  0 | 99
  1 | 00112233
  1 | 666699
  2 | 00112222334444444444
  2 | 66778899999
  3 | 000000111112222222233333333334444
  3 | 5566677778888999
  4 | 0000001111233
  4 | 5555556666666777788888899
  5 | 00000111111122222223444444
  5 | 56667899
  6 | 00233
  6 | 56
  7 | 0001124
  7 | 55899
  8 | 022
  8 | 9
  9 | 
  9 | 5

> 
> 
> 
> cleanEx(); ..nameEx <- "knn2nb"
> 
> ### * knn2nb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: knn2nb
> ### Title: Neighbours list from knn object
> ### Aliases: knn2nb
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> col.knn <- knearneigh(coords, k=4)
> library(maptools)
> plot(polys, border="grey", forcefill=FALSE)
> plot(knn2nb(col.knn), coords, add=TRUE)
> title(main="K nearest neighbours, k = 4")
> 
> 
> 
> cleanEx(); ..nameEx <- "lag.listw"
> 
> ### * lag.listw
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lag.listw
> ### Title: Spatial lag of a numeric vector
> ### Aliases: lag.listw
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> Vx <- lag.listw(nb2listw(COL.nb, style="W"), COL.OLD$CRIME)
> plot(Vx, COL.OLD$CRIME)
> plot(ecdf(COL.OLD$CRIME))
> plot(ecdf(Vx), add=TRUE, col.points="red", col.hor="red")
> 
> 
> 
> cleanEx(); ..nameEx <- "lagsarlm"
> 
> ### * lagsarlm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lagsarlm
> ### Title: Spatial simultaneous autoregressive lag model estimation
> ### Aliases: lagsarlm
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> COL.lag.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb), method="eigen", quiet=FALSE)

Spatial lag model
Jacobian calculated using neighbourhood matrix eigenvalues
Computing eigenvalues ...

(eigen) rho:	 -0.5674437 	function value:	 -202.2909 
(eigen) rho:	 0.03126655 	function value:	 -186.749 
(eigen) rho:	 0.4012898 	function value:	 -182.419 
(eigen) rho:	 0.6138418 	function value:	 -183.5636 
(eigen) rho:	 0.4157662 	function value:	 -182.398 
(eigen) rho:	 0.4295565 	function value:	 -182.3905 
(eigen) rho:	 0.4311288 	function value:	 -182.3904 
(eigen) rho:	 0.4310273 	function value:	 -182.3904 
(eigen) rho:	 0.4310232 	function value:	 -182.3904 
(eigen) rho:	 0.4310232 	function value:	 -182.3904 
(eigen) rho:	 0.4310232 	function value:	 -182.3904 
(eigen) rho:	 0.4310232 	function value:	 -182.3904 
(eigen) rho:	 0.4310232 	function value:	 -182.3904 
> COL.lag.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb, style="W"), method="eigen", quiet=FALSE)

Spatial autoregressive error model
 Jacobian calculated using neighbourhood matrix eigenvalues
Computing eigenvalues ...

(eigen) lambda:	 -0.5674437 	function value:	 -195.8051 
(eigen) lambda:	 0.03126655 	function value:	 -187.0219 
(eigen) lambda:	 0.4012898 	function value:	 -183.8422 
(eigen) lambda:	 0.6299767 	function value:	 -183.4895 
(eigen) lambda:	 0.5811116 	function value:	 -183.3887 
(eigen) lambda:	 0.554104 	function value:	 -183.3817 
(eigen) lambda:	 0.5621834 	function value:	 -183.3805 
(eigen) lambda:	 0.5617028 	function value:	 -183.3805 
(eigen) lambda:	 0.5617888 	function value:	 -183.3805 
(eigen) lambda:	 0.5617902 	function value:	 -183.3805 
(eigen) lambda:	 0.5617903 	function value:	 -183.3805 
(eigen) lambda:	 0.5617903 	function value:	 -183.3805 
> COL.lag.SM <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb), method="SparseM", quiet=FALSE)

Spatial lag model
Jacobian calculated using sparse matrix techniques using SparseM
(SparseM) rho:	 -0.2364499 	function value:	 -204.0209 
(SparseM) rho:	 0.2354499 	function value:	 -191.4847 
(SparseM) rho:	 0.5271001 	function value:	 -187.3391 
(SparseM) rho:	 0.8206424 	function value:	 -189.798 
(SparseM) rho:	 0.5653776 	function value:	 -187.1909 
(SparseM) rho:	 0.5865778 	function value:	 -187.1595 
(SparseM) rho:	 0.5944322 	function value:	 -187.1575 
(SparseM) rho:	 0.5936095 	function value:	 -187.1574 
(SparseM) rho:	 0.593551 	function value:	 -187.1574 
(SparseM) rho:	 0.5935532 	function value:	 -187.1574 
(SparseM) rho:	 0.5935532 	function value:	 -187.1574 
(SparseM) rho:	 0.5935532 	function value:	 -187.1574 
(SparseM) rho:	 -0.2364499 	function value:	 -195.8910 
(SparseM) rho:	 0.2354499 	function value:	 -187.5084 
(SparseM) rho:	 0.5271001 	function value:	 -186.8787 
(SparseM) rho:	 0.4340997 	function value:	 -186.5621 
(SparseM) rho:	 0.4198224 	function value:	 -186.5597 
(SparseM) rho:	 0.4241877 	function value:	 -186.5592 
(SparseM) rho:	 0.4240698 	function value:	 -186.5592 
(SparseM) rho:	 0.4240783 	function value:	 -186.5592 
(SparseM) rho:	 0.4240783 	function value:	 -186.5592 
(SparseM) rho:	 0.4240784 	function value:	 -186.5592 
(SparseM) rho:	 0.4240784 	function value:	 -186.5592 
(SparseM) rho:	 -0.2364499 	function value:	 -192.9523 
(SparseM) rho:	 0.2354499 	function value:	 -183.542 
(SparseM) rho:	 0.5271001 	function value:	 -182.7039 
(SparseM) rho:	 0.4455543 	function value:	 -182.3974 
(SparseM) rho:	 0.4267907 	function value:	 -182.391 
(SparseM) rho:	 0.4311986 	function value:	 -182.3904 
(SparseM) rho:	 0.4310114 	function value:	 -182.3904 
(SparseM) rho:	 0.4310231 	function value:	 -182.3904 
(SparseM) rho:	 0.4310232 	function value:	 -182.3904 
(SparseM) rho:	 0.4310232 	function value:	 -182.3904 
(SparseM) rho:	 0.4310232 	function value:	 -182.3904 
(SparseM) rho:	 0.4310232 	function value:	 -182.3904 
> summary(COL.lag.eig, correlation=TRUE)

Call:
errorsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb, 
    style = "W"), method = "eigen", quiet = FALSE)

Residuals:
      Min        1Q    Median        3Q       Max 
-34.81174  -6.44031  -0.72142   7.61476  23.33626 

Type: error 
Coefficients: (asymptotic standard errors) 
             Estimate Std. Error z value  Pr(>|z|)
(Intercept) 59.893219   5.366163 11.1613 < 2.2e-16
INC         -0.941312   0.330569 -2.8476 0.0044057
HOVAL       -0.302250   0.090476 -3.3407 0.0008358

Lambda: 0.56179 LR test value: 7.9935 p-value: 0.0046945 
Asymptotic standard error: 0.13387 z-value: 4.1966 p-value: 2.7098e-05 
Wald statistic: 17.611 p-value: 2.7098e-05 

Log likelihood: -183.3805 for error model
ML residual variance (sigma squared): 95.575, (sigma: 9.7762)
Number of observations: 49 
Number of parameters estimated: 5 
AIC: 376.76, (AIC for lm: 382.75)

Correlation of Coefficients:
            sigma lambda (Intercept) INC  
lambda      -0.24                         
(Intercept)  0.00  0.00                   
INC          0.00  0.00  -0.56            
HOVAL        0.00  0.00  -0.26       -0.45

> summary(COL.lag.SM, correlation=TRUE)

Call:
lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb), 
    method = "SparseM", quiet = FALSE)

Residuals:
      Min        1Q    Median        3Q       Max 
-37.68585  -5.35636   0.05421   6.02013  23.20555 

Type: lag 
Coefficients: (log likelihood/likelihood ratio) 
              Estimate Log likelihood LR statistic Pr(>|z|)
(Intercept)   45.07925             NA           NA       NA
INC           -1.03162     -187.15742       9.5340 0.002017
HOVAL         -0.26593     -186.55917       8.3375 0.003884

Rho: 0.43102 LR test value: 9.9736 p-value: 0.001588 

Log likelihood: -182.3904 for lag model
ML residual variance (sigma squared): 95.494, (sigma: 9.7721)
Number of observations: 49 
Number of parameters estimated: 5 
AIC: 374.78, (AIC for lm: 382.75)

> COL.lag.B <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb, style="B"))
> summary(COL.lag.B, correlation=TRUE)

Call:
lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb, 
    style = "B"))

Residuals:
     Min       1Q   Median       3Q      Max 
-33.6975  -4.7996  -1.4808   5.3648  25.8922 

Type: lag 
Coefficients: (asymptotic standard errors) 
             Estimate Std. Error z value  Pr(>|z|)
(Intercept) 52.403878   5.961310  8.7907 < 2.2e-16
INC         -1.175261   0.300473 -3.9114 9.178e-05
HOVAL       -0.252680   0.087613 -2.8840  0.003926

Rho: 0.051981 LR test value: 12.764 p-value: 0.00035336 
Asymptotic standard error: 0.014428 z-value: 3.6028 p-value: 0.00031482 
Wald statistic: 12.98 p-value: 0.00031482 

Log likelihood: -180.9953 for lag model
ML residual variance (sigma squared): 93.29, (sigma: 9.6587)
Number of observations: 49 
Number of parameters estimated: 5 
AIC: 371.99, (AIC for lm: 382.75)
LM test for residual autocorrelation
test value: 0.0028047 p-value: 0.95776 

Correlation of Coefficients:
            sigma rho   (Intercept) INC  
rho         -0.04                        
(Intercept)  0.03 -0.74                  
INC         -0.01  0.34 -0.63            
HOVAL        0.00  0.10 -0.30       -0.43

> COL.mixed.B <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb, style="B"), type="mixed", tol.solve=1e-9)
> summary(COL.mixed.B, correlation=TRUE)

Call:
lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb, 
    style = "B"), type = "mixed", tol.solve = 1e-09)

Residuals:
      Min        1Q    Median        3Q       Max 
-34.45813  -5.25361  -0.14753   5.20581  23.81568 

Type: mixed 
Coefficients: (asymptotic standard errors) 
                 Estimate Std. Error z value  Pr(>|z|)
(Intercept)     54.179690   5.817611  9.3130 < 2.2e-16
INC             -0.942199   0.327149 -2.8800  0.003976
HOVAL           -0.287421   0.087377 -3.2894  0.001004
lag.(Intercept) -2.124907   2.756294 -0.7709  0.440749
lag.INC         -0.124606   0.135599 -0.9189  0.358134
lag.HOVAL        0.052373   0.040246  1.3013  0.193150

Rho: 0.08115 LR test value: 3.993 p-value: 0.04569 
Asymptotic standard error: 0.033436 z-value: 2.427 p-value: 0.015224 
Wald statistic: 5.8904 p-value: 0.015224 

Log likelihood: -179.4932 for mixed model
ML residual variance (sigma squared): 85.779, (sigma: 9.2617)
Number of observations: 49 
Number of parameters estimated: 8 
AIC: 374.99, (AIC for lm: 376.98)
LM test for residual autocorrelation
test value: 0.84013 p-value: 0.35936 

Correlation of Coefficients:
                sigma rho   (Intercept) INC   HOVAL lag.(Intercept) lag.INC
rho             -0.16                                                      
(Intercept)      0.02 -0.14                                                
INC             -0.03  0.17 -0.52                                          
HOVAL            0.01 -0.05 -0.28       -0.41                              
lag.(Intercept)  0.14 -0.86 -0.15        0.07  0.12                        
lag.INC         -0.08  0.48  0.00       -0.33  0.10 -0.60                  
lag.HOVAL       -0.03  0.16  0.09        0.11 -0.28 -0.35           -0.39  

> COL.mixed.W <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb, style="W"), type="mixed")
> summary(COL.mixed.W, correlation=TRUE)

Call:
lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb, 
    style = "W"), type = "mixed")

Residuals:
      Min        1Q    Median        3Q       Max 
-37.47829  -6.46731  -0.33835   6.05200  22.62969 

Type: mixed 
Coefficients: (asymptotic standard errors) 
             Estimate Std. Error z value  Pr(>|z|)
(Intercept) 42.822415  12.667205  3.3806 0.0007233
INC         -0.914223   0.331094 -2.7612 0.0057586
HOVAL       -0.293738   0.089212 -3.2926 0.0009927
lag.INC     -0.520284   0.565129 -0.9206 0.3572355
lag.HOVAL    0.245640   0.178917  1.3729 0.1697756

Rho: 0.42634 LR test value: 5.3693 p-value: 0.020494 
Asymptotic standard error: 0.15623 z-value: 2.7288 p-value: 0.0063561 
Wald statistic: 7.4465 p-value: 0.0063561 

Log likelihood: -181.3935 for mixed model
ML residual variance (sigma squared): 91.791, (sigma: 9.5808)
Number of observations: 49 
Number of parameters estimated: 7 
AIC: 376.79, (AIC for lm: 380.16)
LM test for residual autocorrelation
test value: 0.28919 p-value: 0.59074 

Correlation of Coefficients:
            sigma rho   (Intercept) INC   HOVAL lag.INC
rho         -0.18                                      
(Intercept)  0.16 -0.89                                
INC         -0.03  0.14 -0.19                          
HOVAL        0.02 -0.09  0.03       -0.45              
lag.INC     -0.09  0.49 -0.53       -0.36  0.05        
lag.HOVAL   -0.04  0.19 -0.36        0.19 -0.24 -0.41  

> NA.COL.OLD <- COL.OLD
> NA.COL.OLD$CRIME[20:25] <- NA
> COL.lag.NA <- lagsarlm(CRIME ~ INC + HOVAL, data=NA.COL.OLD,
+  nb2listw(COL.nb), na.action=na.exclude, tol.opt=.Machine$double.eps^0.4)
> COL.lag.NA$na.action
1020 1021 1022 1023 1024 1025 
  20   21   22   23   24   25 
attr(,"class")
[1] "exclude"
> COL.lag.NA

Call:
lagsarlm(formula = CRIME ~ INC + HOVAL, data = NA.COL.OLD, listw = nb2listw(COL.nb), 
    na.action = na.exclude, tol.opt = .Machine$double.eps^0.4)
Type: lag 

Coefficients:
(Intercept)         INC       HOVAL         rho 
 43.1054975  -0.9267352  -0.2715541   0.4537820 

Log likelihood: -160.8867 
> resid(COL.lag.NA)
       1001        1002        1003        1004        1005        1006 
 -4.4352945 -13.2750948  -2.9233555 -37.3067542   1.3568011  -3.8828027 
       1007        1008        1009        1010        1011        1012 
  5.9980436 -12.8113318  -4.0482558  18.1813323   5.9714203   1.0035599 
       1013        1014        1015        1016        1017        1018 
 -1.7490666  -1.7490651   5.8456327  10.1074158  -4.3706895   3.3713771 
       1019        1020        1021        1022        1023        1024 
 -4.0823022          NA          NA          NA          NA          NA 
       1025        1026        1027        1028        1029        1030 
         NA  -6.0553296 -11.5813311  -8.0011389  -1.9047478   3.9744243 
       1031        1032        1033        1034        1035        1036 
  4.8148614   6.0673483  10.2059847  22.7419913  -2.0830998   0.1422777 
       1037        1038        1039        1040        1041        1042 
  8.6436388   8.8150864   6.4974685  15.4121789   9.4182148   5.6427603 
       1043        1044        1045        1046        1047        1048 
 -7.5727123  -7.5983733  -9.7792620 -10.0870764  -3.1242393   3.4921796 
       1049 
  0.7173251 
> 
> 
> 
> cleanEx(); ..nameEx <- "listw2sn"
> 
> ### * listw2sn
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: listw2sn
> ### Title: Spatial neighbour sparse representation
> ### Aliases: listw2sn sn2listw
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> col.listw <- nb2listw(col.gal.nb)
> col.listw$neighbours[[1]]
[1] 2 3
> col.listw$weights[[1]]
[1] 0.5 0.5
> col.sn <- listw2sn(col.listw)
> str(col.sn)
Classes spatial.neighbour  and `data.frame':	230 obs. of  3 variables:
 $ from   : int  1 1 2 2 2 3 3 3 3 4 ...
 $ to     : int  2 3 1 3 4 1 2 4 5 2 ...
 $ weights: num  0.500 0.500 0.333 0.333 0.333 ...
 - attr(*, "n")= int 49
 - attr(*, "region.id")= num  1005 1001 1006 1002 1007 ...
 - attr(*, "neighbours.attrs")= chr  "class" "region.id" "gal" "call" ...
 - attr(*, "weights.attrs")= chr  "mode" "W" "comp"
 - attr(*, "listw.call")= language nb2listw(neighbours = col.gal.nb)
> W <- asMatrixCsrListw(similar.listw(col.listw))
> str(W)
Formal class 'matrix.csr' [package "SparseM"] with 4 slots
  ..@ ra       : num [1:230] 0.408 0.354 0.408 0.289 0.289 ...
  ..@ ja       : int [1:230] 2 3 1 3 4 1 2 4 5 2 ...
  ..@ ia       : int [1:50] 1 3 6 10 14 21 23 27 33 41 ...
  ..@ dimension: int [1:2] 49 49
> rho <- seq(-0.8, 0.9, 0.1)
> for (i in rho) print(paste("rho:", i, "log(det(I - rho*W))",
+   log(det(asMatrixCsrIrW(W, i)))), quote=TRUE)
[1] "rho: -0.8 log(det(I - rho*W)) -3.32243407978180"
[1] "rho: -0.7 log(det(I - rho*W)) -2.52453311812212"
[1] "rho: -0.6 log(det(I - rho*W)) -1.84841461424027"
[1] "rho: -0.5 log(det(I - rho*W)) -1.28423182869652"
[1] "rho: -0.4 log(det(I - rho*W)) -0.825408693950342"
[1] "rho: -0.3 log(det(I - rho*W)) -0.468020827352672"
[1] "rho: -0.2 log(det(I - rho*W)) -0.210481644636056"
[1] "rho: -0.1 log(det(I - rho*W)) -0.0534583888635971"
[1] "rho: 0 log(det(I - rho*W)) 0"
[1] "rho: 0.1 log(det(I - rho*W)) -0.0559069320516246"
[1] "rho: 0.2 log(det(I - rho*W)) -0.230433425962048"
[1] "rho: 0.3 log(det(I - rho*W)) -0.537514700112025"
[1] "rho: 0.4 log(det(I - rho*W)) -0.99791717000465"
[1] "rho: 0.5 log(det(I - rho*W)) -1.64318107245676"
[1] "rho: 0.6 log(det(I - rho*W)) -2.52345398161187"
[1] "rho: 0.7 log(det(I - rho*W)) -3.72509399156610"
[1] "rho: 0.8 log(det(I - rho*W)) -5.41872816510602"
[1] "rho: 0.9 log(det(I - rho*W)) -8.04718926152849"
> 
> 
> 
> cleanEx(); ..nameEx <- "lm.LMtests"
> 
> ### * lm.LMtests
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lm.LMtests
> ### Title: Lagrange Multiplier diagnostics for spatial dependence in linear
> ###   models
> ### Aliases: lm.LMtests print.LMtestlist
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD)
> summary(oldcrime.lm)

Call:
lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)

Residuals:
    Min      1Q  Median      3Q     Max 
-34.418  -6.388  -1.580   9.052  28.649 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  68.6190     4.7355  14.490  < 2e-16 ***
HOVAL        -0.2739     0.1032  -2.654   0.0109 *  
INC          -1.5973     0.3341  -4.780 1.83e-05 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 11.43 on 46 degrees of freedom
Multiple R-Squared: 0.5524,	Adjusted R-squared: 0.5329 
F-statistic: 28.39 on 2 and 46 DF,  p-value: 9.34e-09 

> lm.LMtests(oldcrime.lm, nb2listw(COL.nb), test=c("LMerr", "LMlag", "RLMerr",
+   "RLMlag", "SARMA"))

	Lagrange multiplier diagnostics for spatial dependence

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb)
 
LMerr = 5.7231, df = 1, p-value = 0.01674


	Lagrange multiplier diagnostics for spatial dependence

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb)
 
LMlag = 9.3637, df = 1, p-value = 0.002213


	Lagrange multiplier diagnostics for spatial dependence

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb)
 
RLMerr = 0.0795, df = 1, p-value = 0.778


	Lagrange multiplier diagnostics for spatial dependence

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb)
 
RLMlag = 3.72, df = 1, p-value = 0.05376


	Lagrange multiplier diagnostics for spatial dependence

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb)
 
SARMA = 9.4432, df = 2, p-value = 0.008901

> 
> 
> 
> cleanEx(); ..nameEx <- "lm.morantest"
> 
> ### * lm.morantest
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lm.morantest
> ### Title: Moran's I test for residual spatial autocorrelation
> ### Aliases: lm.morantest listw2U
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> oldcrime1.lm <- lm(CRIME ~ 1, data = COL.OLD)
> oldcrime.lm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD)
> lm.morantest(oldcrime.lm, nb2listw(COL.nb, style="W"))

	Global Moran's I for regression residuals

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb, style = "W")
 
Moran I statistic standard deviate = 2.9539, p-value = 0.001569
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
       0.235638354       -0.033302866        0.008289408 

> lm.LMtests(oldcrime.lm, nb2listw(COL.nb, style="W"))

	Lagrange multiplier diagnostics for spatial dependence

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb, style = "W")
 
LMerr = 5.7231, df = 1, p-value = 0.01674

> lm.morantest(oldcrime.lm, nb2listw(COL.nb, style="S"))

	Global Moran's I for regression residuals

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD)
weights: nb2listw(COL.nb, style = "S")
 
Moran I statistic standard deviate = 3.1745, p-value = 0.0007504
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
       0.239317561       -0.033431740        0.007381982 

> lm.morantest(oldcrime1.lm, nb2listw(COL.nb, style="W"))

	Global Moran's I for regression residuals

data:  
model: lm(formula = CRIME ~ 1, data = COL.OLD)
weights: nb2listw(COL.nb, style = "W")
 
Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
       0.510951264       -0.020833333        0.008779831 

> moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb, style="W"),
+  randomisation=FALSE)

	Moran's I test under normality

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(COL.nb, style = "W")  
 
Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.510951264      -0.020833333       0.008779831 

> oldcrime.wlm <- lm(CRIME ~ HOVAL + INC, data = COL.OLD, weights = I(1/AREA))
> lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style="W"), resfun=weighted.residuals)

	Global Moran's I for regression residuals

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights =
I(1/AREA))
weights: nb2listw(COL.nb, style = "W")
 
Moran I statistic standard deviate = 3.0141, p-value = 0.001289
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
       0.241298974       -0.032224366        0.008235091 

> lm.morantest(oldcrime.wlm, nb2listw(COL.nb, style="W"), resfun=rstudent)

	Global Moran's I for regression residuals

data:  
model: lm(formula = CRIME ~ HOVAL + INC, data = COL.OLD, weights =
I(1/AREA))
weights: nb2listw(COL.nb, style = "W")
 
Moran I statistic standard deviate = 2.822, p-value = 0.002387
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
       0.223860298       -0.032224366        0.008235091 

> 
> 
> 
> cleanEx(); ..nameEx <- "lm.morantest.sad"
> 
> ### * lm.morantest.sad
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: lm.morantest.sad
> ### Title: Saddlepoint approximation of global Moran's I test
> ### Aliases: lm.morantest.sad print.moransad summary.moransad
> ###   print.summary.moransad
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(eire)
> e.lm <- lm(OWNCONS ~ ROADACC, data=eire.df)
> lm.morantest(e.lm, nb2listw(eire.nb))

	Global Moran's I for regression residuals

data:  
model: lm(formula = OWNCONS ~ ROADACC, data = eire.df)
weights: nb2listw(eire.nb)
 
Moran I statistic standard deviate = 3.2575, p-value = 0.0005619
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
        0.33660565        -0.05877741         0.01473183 

> lm.morantest.sad(e.lm, nb2listw(eire.nb))

	Saddlepoint approximation for global Moran's I (Barndorff-Nielsen
	formula)

data:  
model:lm(formula = OWNCONS ~ ROADACC, data = eire.df)
weights: nb2listw(eire.nb)
 
Saddlepoint approximation = 2.9395, p-value = 0.001644
alternative hypothesis: greater 
sample estimates:
Observed Moran's I 
         0.3366057 

> summary(lm.morantest.sad(e.lm, nb2listw(eire.nb)))

	Saddlepoint approximation for global Moran's I (Barndorff-Nielsen
	formula)

data:  
model:lm(formula = OWNCONS ~ ROADACC, data = eire.df)
weights: nb2listw(eire.nb)
 
Saddlepoint approximation = 2.9395, p-value = 0.001644
alternative hypothesis: greater 
sample estimates:
Observed Moran's I 
         0.3366057 

 Expectation     Variance Std. deviate     Skewness     Kurtosis      Minimum 
 -0.05877741   0.01473183   3.25753938   0.31336881   3.05047361  -0.67545810 
     Maximum        omega        sad.r        sad.u 
  0.89091555   0.76549075   2.77616585   4.36854629 
      f.root         iter   estim.prec 
6.916689e-14 1.100000e+01 7.450581e-09 
> e.wlm <- lm(OWNCONS ~ ROADACC, data=eire.df, weights=RETSALE)
> lm.morantest(e.wlm, nb2listw(eire.nb), resfun=rstudent)

	Global Moran's I for regression residuals

data:  
model: lm(formula = OWNCONS ~ ROADACC, data = eire.df, weights =
RETSALE)
weights: nb2listw(eire.nb)
 
Moran I statistic standard deviate = 3.1385, p-value = 0.0008491
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
        0.34500329        -0.04049313         0.01508687 

> lm.morantest.sad(e.wlm, nb2listw(eire.nb), resfun=rstudent)

	Saddlepoint approximation for global Moran's I (Barndorff-Nielsen
	formula)

data:  
model:lm(formula = OWNCONS ~ ROADACC, data = eire.df, weights = RETSALE)
weights: nb2listw(eire.nb)
 
Saddlepoint approximation = 2.8708, p-value = 0.002047
alternative hypothesis: greater 
sample estimates:
Observed Moran's I 
         0.3450033 

> 
> 
> 
> cleanEx(); ..nameEx <- "localG"
> 
> ### * localG
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: localG
> ### Title: G and Gstar local spatial statistics
> ### Aliases: localG
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(getisord)
> xycoords <- cbind(xyz$x, xyz$y)
> nb30 <- dnearneigh(xycoords, 0, 30)
> G30 <- localG(spNamedVec("val", xyz), nb2listw(nb30, style="B"))
> G30[length(xyz$val)-136]
     120 
1.221979 
> nb60 <- dnearneigh(xycoords, 0, 60)
> G60 <- localG(spNamedVec("val", xyz), nb2listw(nb60, style="B"))
> G60[length(xyz$val)-136]
     120 
1.748098 
> nb90 <- dnearneigh(xycoords, 0, 90)
> G90 <- localG(spNamedVec("val", xyz), nb2listw(nb90, style="B"))
> G90[length(xyz$val)-136]
     120 
1.986135 
> nb120 <- dnearneigh(xycoords, 0, 120)
> G120 <- localG(spNamedVec("val", xyz), nb2listw(nb120, style="B"))
> G120[length(xyz$val)-136]
     120 
1.893374 
> nb150 <- dnearneigh(xycoords, 0, 150)
> G150 <- localG(spNamedVec("val", xyz), nb2listw(nb150, style="B"))
> G150[length(xyz$val)-136]
     120 
1.237454 
> brks <- seq(-5,5,1)
> cm.col <- cm.colors(length(brks)-1)
> image(x, y, t(matrix(G30, nrow=16, ncol=16, byrow=TRUE)),
+   breaks=brks, col=cm.col, asp=1)
> text(xyz$x, xyz$y, round(G30, digits=1), cex=0.7)
> polygon(c(195,225,225,195), c(195,195,225,225), lwd=2)
> title(main=expression(paste("Values of the ", G[i], " statistic")))
> G30s <- localG(spNamedVec("val", xyz), nb2listw(include.self(nb30),
+  style="B"))
> cat("value according to Getis and Ord's eq. 14.2, p. 263 (1996)\n")
value according to Getis and Ord's eq. 14.2, p. 263 (1996)
> G30s[length(xyz$val)-136]
[1] 1.450780
> cat(paste("value given by Getis and Ord (1996), p. 267",
+   "(division by n-1 rather than n \n in variance)\n"))
value given by Getis and Ord (1996), p. 267 (division by n-1 rather than n 
 in variance)
> G30s[length(xyz$val)-136] *
+   (sqrt(sum(scale(xyz$val, scale=FALSE)^2)/length(xyz$val)) /
+   sqrt(var(xyz$val)))
[1] 1.447943
> image(x, y, t(matrix(G30s, nrow=16, ncol=16, byrow=TRUE)),
+   breaks=brks, col=cm.col, asp=1)
> text(xyz$x, xyz$y, round(G30s, digits=1), cex=0.7)
> polygon(c(195,225,225,195), c(195,195,225,225), lwd=2)
> title(main=expression(paste("Values of the ", G[i]^"*", " statistic")))
> 
> 
> 
> cleanEx(); ..nameEx <- "localmoran"
> 
> ### * localmoran
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: localmoran
> ### Title: Local Moran's I statistic
> ### Aliases: localmoran
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(afcon)
> oid <- order(afcon$id)
> resI <- localmoran(spNamedVec("totcon", afcon), nb2listw(paper.nb))
> printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]), check.names=FALSE)
                                 Ii       E.Ii     Var.Ii       Z.Ii Pr.z...0.
THE GAMBIA                0.3752254 -0.0243902  0.8707799  0.4282410    0.3342
MALI                      0.4636340 -0.0243902  0.1084938  1.4816272    0.0692
SENEGAL                   0.2567014 -0.0243902  0.2037796  0.6226838    0.2667
BENIN                     0.1941194 -0.0243902  0.2037796  0.4840501    0.3142
MAURITANIA                0.0970535 -0.0243902  0.2037796  0.2690263    0.3940
NIGER                     0.2307143 -0.0243902  0.1084938  0.7744898    0.2193
IVORY COAST               0.2900359 -0.0243902  0.1593129  0.7877586    0.2154
GUINEA                    0.1826275 -0.0243902  0.1593129  0.5186592    0.3020
BURKINA FASO              0.5082778 -0.0243902  0.1296684  1.4792430    0.0695
LIBERIA                   0.1856475 -0.0243902  0.2778907  0.3984375    0.3452
SIERRA LEONE              0.2652337 -0.0243902  0.4261130  0.4436823    0.3286
GHANA                     0.1476406 -0.0243902  0.2778907  0.3263392    0.3721
TOGO                      0.2193448 -0.0243902  0.2778907  0.4623607    0.3219
CAMEROON                  0.2592454 -0.0243902  0.1593129  0.7106167    0.2387
NIGERIA                   0.1137709 -0.0243902  0.2037796  0.3060593    0.3798
GABON                     0.2036649 -0.0243902  0.4261130  0.3493635    0.3634
CENTRAL AFRICAN REPUBLIC -0.4420567 -0.0243902  0.1593129 -1.0464153    0.8523
CHAD                     -0.1052846 -0.0243902  0.1296684 -0.2246472    0.5889
CONGO                     0.0113803 -0.0243902  0.2037796  0.0792401    0.4684
ZAIRE                     0.7097807 -0.0243902  0.0802610  2.5914625    0.0048
ANGOLA                    0.1179749 -0.0243902  0.2778907  0.2700640    0.3936
UGANDA                    1.9425080 -0.0243902  0.1593129  4.9278382 4.157e-07
KENYA                     1.1969287 -0.0243902  0.1593129  3.0598747    0.0011
TANZANIA                  0.2718545 -0.0243902  0.0926129  0.9734529    0.1652
BURUNDI                  -0.4842787 -0.0243902  0.2778907 -0.8723997    0.8085
RWANDA                   -0.7523578 -0.0243902  0.2037796 -1.6126187    0.9466
SOMALIA                   0.4527658 -0.0243902  0.4261130  0.7309674    0.2324
ETHIOPIA                  0.7251240 -0.0243902  0.2778907  1.4218143    0.0775
ZAMBIA                    0.0421598 -0.0243902  0.0926129  0.2186818    0.4134
ZIMBABWE                 -0.0095068 -0.0243902  0.2037796  0.0329703    0.4868
MALAWI                   -0.2288840 -0.0243902  0.2778907 -0.3879207    0.6510
MOZAMBIQUE                0.0167900 -0.0243902  0.1296684  0.1143594    0.4545
SOUTH AFRICA             -0.1825396 -0.0243902  0.1084938 -0.4801368    0.6844
LESOTHO                  -0.4193478 -0.0243902  0.8707799 -0.4232493    0.6639
BOTSWANA                 -0.0039316 -0.0243902  0.2778907  0.0388096    0.4845
SWAZILAND                 0.0166842 -0.0243902  0.4261130  0.0629231    0.4749
MOROCCO                  -0.0969607 -0.0243902  0.4261130 -0.1111725    0.5443
ALGERIA                  -0.0100369 -0.0243902  0.1296684  0.0398599    0.4841
TUNISIA                   0.0053873 -0.0243902  0.4261130  0.0456170    0.4818
LIBYA                     0.8038237 -0.0243902  0.1296684  2.2999872    0.0107
SUDAN                     2.9877738 -0.0243902  0.0926129  9.8978982 2.126e-23
EGYPT                     6.9467291 -0.0243902  0.4261130 10.6792343 6.366e-27
> hist(resI[,5])
> resI <- localmoran(spNamedVec("totcon", afcon), nb2listw(paper.nb), p.adjust.method="bonferroni")
> printCoefmat(data.frame(resI[oid,], row.names=afcon$name[oid]), check.names=FALSE)
                                 Ii       E.Ii     Var.Ii       Z.Ii Pr.z...0.
THE GAMBIA                0.3752254 -0.0243902  0.8707799  0.4282410    0.6685
MALI                      0.4636340 -0.0243902  0.1084938  1.4816272    0.5538
SENEGAL                   0.2567014 -0.0243902  0.2037796  0.6226838    1.0000
BENIN                     0.1941194 -0.0243902  0.2037796  0.4840501    1.0000
MAURITANIA                0.0970535 -0.0243902  0.2037796  0.2690263    1.0000
NIGER                     0.2307143 -0.0243902  0.1084938  0.7744898    1.0000
IVORY COAST               0.2900359 -0.0243902  0.1593129  0.7877586    1.0000
GUINEA                    0.1826275 -0.0243902  0.1593129  0.5186592    1.0000
BURKINA FASO              0.5082778 -0.0243902  0.1296684  1.4792430    0.4868
LIBERIA                   0.1856475 -0.0243902  0.2778907  0.3984375    1.0000
SIERRA LEONE              0.2652337 -0.0243902  0.4261130  0.4436823    0.9859
GHANA                     0.1476406 -0.0243902  0.2778907  0.3263392    1.0000
TOGO                      0.2193448 -0.0243902  0.2778907  0.4623607    1.0000
CAMEROON                  0.2592454 -0.0243902  0.1593129  0.7106167    1.0000
NIGERIA                   0.1137709 -0.0243902  0.2037796  0.3060593    1.0000
GABON                     0.2036649 -0.0243902  0.4261130  0.3493635    1.0000
CENTRAL AFRICAN REPUBLIC -0.4420567 -0.0243902  0.1593129 -1.0464153    1.0000
CHAD                     -0.1052846 -0.0243902  0.1296684 -0.2246472    1.0000
CONGO                     0.0113803 -0.0243902  0.2037796  0.0792401    1.0000
ZAIRE                     0.7097807 -0.0243902  0.0802610  2.5914625    0.0478
ANGOLA                    0.1179749 -0.0243902  0.2778907  0.2700640    1.0000
UGANDA                    1.9425080 -0.0243902  0.1593129  4.9278382 2.494e-06
KENYA                     1.1969287 -0.0243902  0.1593129  3.0598747    0.0066
TANZANIA                  0.2718545 -0.0243902  0.0926129  0.9734529    1.0000
BURUNDI                  -0.4842787 -0.0243902  0.2778907 -0.8723997    1.0000
RWANDA                   -0.7523578 -0.0243902  0.2037796 -1.6126187    1.0000
SOMALIA                   0.4527658 -0.0243902  0.4261130  0.7309674    0.6972
ETHIOPIA                  0.7251240 -0.0243902  0.2778907  1.4218143    0.3102
ZAMBIA                    0.0421598 -0.0243902  0.0926129  0.2186818    1.0000
ZIMBABWE                 -0.0095068 -0.0243902  0.2037796  0.0329703    1.0000
MALAWI                   -0.2288840 -0.0243902  0.2778907 -0.3879207    1.0000
MOZAMBIQUE                0.0167900 -0.0243902  0.1296684  0.1143594    1.0000
SOUTH AFRICA             -0.1825396 -0.0243902  0.1084938 -0.4801368    1.0000
LESOTHO                  -0.4193478 -0.0243902  0.8707799 -0.4232493    1.0000
BOTSWANA                 -0.0039316 -0.0243902  0.2778907  0.0388096    1.0000
SWAZILAND                 0.0166842 -0.0243902  0.4261130  0.0629231    1.0000
MOROCCO                  -0.0969607 -0.0243902  0.4261130 -0.1111725    1.0000
ALGERIA                  -0.0100369 -0.0243902  0.1296684  0.0398599    1.0000
TUNISIA                   0.0053873 -0.0243902  0.4261130  0.0456170    1.0000
LIBYA                     0.8038237 -0.0243902  0.1296684  2.2999872    0.0751
SUDAN                     2.9877738 -0.0243902  0.0926129  9.8978982 1.913e-22
EGYPT                     6.9467291 -0.0243902  0.4261130 10.6792343 1.910e-26
> hist(resI[,5])
> totcon <- spNamedVec("totcon", afcon)
> is.na(totcon) <- sample(1:length(totcon), 5)
> totcon
  TS   AG   MO   LY   EG   MR   ML   NG   CD   SU   ET   SG   UV   NI   GA   CM 
1363 1421 1861 2355 5246  811  299   NA  895 4751 1878   NA  347 1130  241   NA 
  GV   BN   SO   GH   TO   CT   IV   SL   LI   CG   KE   UG   CF   GB   TZ   RW 
1015  998 2122 1090  848  618   NA  423  980 3087 2273 3134 1142  824 2881  487 
  BY   AO   ZA   MI   MZ   ZI   BC   SF   WZ   LT 
 604 1528 1554   NA  792  795 1266 1875  147  363 
> resI.na <- localmoran(totcon, nb2listw(paper.nb), na.action=na.exclude,
+  zero.policy=TRUE)
> if (class(attr(resI.na, "na.action")) == "exclude") {
+  print(data.frame(resI.na[oid,], row.names=afcon$name[oid]), digits=2)
+ } else print(resI.na, digits=2)
                              Ii   E.Ii Var.Ii     Z.Ii Pr.z...0.
THE GAMBIA                0.0000  0.000  0.000      NaN       NaN
MALI                      0.4726 -0.028  0.202  1.11364   1.3e-01
SENEGAL                       NA     NA     NA       NA        NA
BENIN                     0.2259 -0.028  0.276  0.48257   3.1e-01
MAURITANIA                0.1201 -0.028  0.276  0.28125   3.9e-01
NIGER                         NA     NA     NA       NA        NA
IVORY COAST                   NA     NA     NA       NA        NA
GUINEA                    0.2847 -0.028  0.276  0.59444   2.8e-01
BURKINA FASO              0.5273 -0.028  0.202  1.23523   1.1e-01
LIBERIA                   0.2546 -0.028  0.425  0.43318   3.3e-01
SIERRA LEONE              0.3450 -0.028  0.425  0.57183   2.8e-01
GHANA                     0.2269 -0.028  0.425  0.39060   3.5e-01
TOGO                      0.2852 -0.028  0.276  0.59551   2.8e-01
CAMEROON                      NA     NA     NA       NA        NA
NIGERIA                   0.1183 -0.028  0.425  0.22411   4.1e-01
GABON                     0.1418 -0.028  0.871  0.18168   4.3e-01
CENTRAL AFRICAN REPUBLIC -0.6398 -0.028  0.202 -1.36207   9.1e-01
CHAD                     -0.3194 -0.028  0.202 -0.64892   7.4e-01
CONGO                    -0.0149 -0.028  0.276  0.02448   4.9e-01
ZAIRE                     0.5103 -0.028  0.078  1.92726   2.7e-02
ANGOLA                    0.0460 -0.028  0.276  0.14027   4.4e-01
UGANDA                    1.5980 -0.028  0.157  4.09940   2.1e-05
KENYA                     0.9448 -0.028  0.157  2.45251   7.1e-03
TANZANIA                  0.2823 -0.028  0.106  0.95116   1.7e-01
BURUNDI                  -0.4492 -0.028  0.276 -0.80181   7.9e-01
RWANDA                   -0.7107 -0.028  0.202 -1.51973   9.4e-01
SOMALIA                   0.3232 -0.028  0.425  0.53830   3.0e-01
ETHIOPIA                  0.5257 -0.028  0.276  1.05296   1.5e-01
ZAMBIA                    0.0250 -0.028  0.106  0.16189   4.4e-01
ZIMBABWE                  0.0357 -0.028  0.202  0.14121   4.4e-01
MALAWI                        NA     NA     NA       NA        NA
MOZAMBIQUE               -0.0029 -0.028  0.157  0.06262   4.8e-01
SOUTH AFRICA             -0.1704 -0.028  0.106 -0.43759   6.7e-01
LESOTHO                  -0.3519 -0.028  0.871 -0.34725   6.4e-01
BOTSWANA                  0.0049 -0.028  0.276  0.06219   4.8e-01
SWAZILAND                 0.1088 -0.028  0.425  0.20946   4.2e-01
MOROCCO                  -0.1034 -0.028  0.425 -0.11600   5.5e-01
ALGERIA                   0.0019 -0.028  0.157  0.07481   4.7e-01
TUNISIA                  -0.0273 -0.028  0.425  0.00073   5.0e-01
LIBYA                     0.8883 -0.028  0.157  2.30998   1.0e-02
SUDAN                     2.4774 -0.028  0.090  8.33526   3.9e-17
EGYPT                     6.0584 -0.028  0.425  9.33517   5.0e-21
> resG <- localG(spNamedVec("totcon", afcon), nb2listw(include.self(paper.nb)))
> print(data.frame(resG[oid], row.names=afcon$name[oid]), digits=2)
                         resG.oid.
THE GAMBIA                  -0.984
MALI                        -1.699
SENEGAL                     -1.463
BENIN                       -1.301
MAURITANIA                  -0.605
NIGER                       -1.049
IVORY COAST                 -1.417
GUINEA                      -1.449
BURKINA FASO                -1.751
LIBERIA                     -1.041
SIERRA LEONE                -0.870
GHANA                       -1.103
TOGO                        -0.991
CAMEROON                    -1.133
NIGERIA                     -1.173
GABON                       -0.789
CENTRAL AFRICAN REPUBLIC     1.173
CHAD                         0.463
CONGO                       -0.203
ZAIRE                        2.023
ANGOLA                       1.235
UGANDA                       3.336
KENYA                        3.503
TANZANIA                     1.098
BURUNDI                      0.774
RWANDA                       1.457
SOMALIA                      1.183
ETHIOPIA                     2.627
ZAMBIA                       0.753
ZIMBABWE                    -0.200
MALAWI                       0.212
MOZAMBIQUE                  -0.288
SOUTH AFRICA                -0.868
LESOTHO                     -0.298
BOTSWANA                     0.041
SWAZILAND                   -0.659
MOROCCO                      0.022
ALGERIA                     -0.363
TUNISIA                      0.579
LIBYA                        2.553
SUDAN                        4.039
EGYPT                        4.421
> 
> 
> 
> 
> cleanEx(); ..nameEx <- "localmoran.sad"
> 
> ### * localmoran.sad
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: localmoran.sad
> ### Title: Saddlepoint approximation of local Moran's Ii tests
> ### Aliases: localmoran.sad listw2star print.summary.localmoransad
> ###   summary.localmoransad print.localmoransad as.data.frame.localmoransad
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(eire)
> e.lm <- lm(OWNCONS ~ ROADACC, data=eire.df)
> e.locmor <- summary(localmoran.sad(e.lm, eire.nb, select=1:nrow(eire.df)))
> e.locmor
             Local Morans I Stand. dev. (N)      Pr. (N) Saddlepoint
1 Carlow        0.216996683      0.74177148 2.291129e-01  0.95074844
2 Cavan        -0.372573613     -0.81297374 7.918834e-01 -1.00603119
3 Clare         0.231975105      0.49502499 3.102912e-01  0.67166518
4 Cork          0.781935479      1.75999915 3.920398e-02  1.74761575
5 Donegal      -1.690640590     -1.98244914 9.762855e-01 -1.72031078
6 Dublin       -0.160696921     -0.15041940 5.597831e-01 -0.35212627
7 Galway        1.313714727      3.34305297 4.143104e-04  2.66849536
8 Kerry         0.365348659      0.58147812 2.804591e-01  0.78073279
9 Kildare      -0.025575445      0.15146558 4.398042e-01  0.04167665
10 Kilkenny     0.576843308      1.62868431 5.168993e-02  1.70897697
11 Laoghis     -0.059517978      0.01724651 4.931200e-01 -0.12155465
12 Leitrim      0.384845866      1.27548777 1.010683e-01  1.47227033
13 Limerick     0.118179867      0.34038037 3.667850e-01  0.45727712
14 Longford     1.416432004      3.10732224 9.439524e-04  2.51113769
15 Louth        0.562429203      0.87665682 1.903365e-01  1.07441571
16 Mayo         0.875727038      2.02375701 2.149758e-02  2.05251226
17 Meath        0.003678560      0.16081712 4.361187e-01  0.12813539
18 Monaghan     0.550983111      1.06684464 1.430210e-01  1.23999193
19 Offaly       0.151555560      0.61933942 2.678464e-01  0.80786519
20 Roscommon    2.043688390      6.66107106 1.359196e-11  4.53187292
21 Sligo       -0.475798710     -0.73430274 7.686179e-01 -0.94578114
22 Tipperary   -0.034541063      0.04843351 4.806854e-01 -0.06919691
23 Waterford    0.857234228      1.98516133 2.356326e-02  1.91385108
24 Westmeath    0.451385718      1.20305006 1.144785e-01  1.36017204
25 Wexford      0.643718339      1.55468550 6.001049e-02  1.63188492
26 Wicklow      0.024419502      0.21823347 4.136236e-01  0.21197000
                Pr. (Sad) Expectation   Variance   Skewness Kurtosis    Minimum
1 Carlow     1.708660e-01 -0.06471134 0.14423085 -0.7895263 7.059116  -5.461326
2 Cavan      8.427997e-01 -0.04030838 0.16703857 -0.4622793 6.813004  -5.567356
3 Clare      2.508984e-01 -0.04219377 0.30674823 -0.3579185 6.761932  -7.406885
4 Cork       4.026529e-02 -0.04363826 0.22003250 -0.4363325 6.799081  -6.360927
5 Donegal    9.573120e-01 -0.11935726 0.62821008 -0.7004303 6.979051 -11.236382
6 Dublin     6.376282e-01 -0.08240217 0.27093033 -0.7352902 7.009201  -7.420687
7 Galway     3.809592e-03 -0.04389010 0.16491503 -0.5059997 6.838308  -5.573707
8 Kerry      2.174798e-01 -0.03212369 0.46724761 -0.2212594 6.714810  -8.915104
9 Kildare    4.833782e-01 -0.07623733 0.11187546 -1.0416026 7.339962  -4.999621
10 Kilkenny  4.372761e-02 -0.05911601 0.15247016 -0.7040737 6.982131  -5.538889
11 Laoghis   5.483741e-01 -0.06620117 0.15016408 -0.7915137 7.061015  -5.574277
12 Leitrim   7.047395e-02 -0.06828680 0.12621127 -0.8864130 7.157471  -5.186756
13 Limerick  3.237359e-01 -0.04172917 0.22070746 -0.4167943 6.789132  -6.348870
14 Longford  6.017137e-03 -0.04055162 0.21985521 -0.4059156 6.783792  -6.324457
15 Louth     1.413182e-01 -0.04386717 0.47831137 -0.2983105 6.738631  -9.149779
16 Mayo      2.005995e-02 -0.10340651 0.23408152 -0.9804377 7.264328  -7.165847
17 Meath     4.490209e-01 -0.04799533 0.10324707 -0.6949022 6.974408  -4.551176
18 Monaghan  1.074892e-01 -0.04136950 0.30828917 -0.3501006 6.758633  -7.415047
19 Offaly    2.095841e-01 -0.04662212 0.10238870 -0.6782821 6.960676  -4.519986
20 Roscommon 2.923151e-06 -0.04435301 0.09826301 -0.6591526 6.945294  -4.414164
21 Sligo     8.278699e-01 -0.11041170 0.24760301 -1.0156782 7.307311  -7.409091
22 Tipperary 5.275836e-01 -0.04872132 0.08571886 -0.7716947 7.042300  -4.198353
23 Waterford 2.781959e-02 -0.05435079 0.21086415 -0.5533724 6.868342  -6.353514
24 Westmeath 8.688774e-02 -0.04181671 0.16806722 -0.4779156 6.821788  -5.599610
25 Wexford   5.135187e-02 -0.05432673 0.20159596 -0.5654870 6.876461  -6.225016
26 Wicklow   4.160652e-01 -0.07022471 0.18808122 -0.7515626 7.023792  -6.198974
              Maximum        omega       sad.r       sad.u
1 Carlow     3.908254  0.071122863  0.71853146  0.84900467
2 Cavan      4.599954 -0.051532330 -0.69003582 -0.85816092
3 Clare      6.394234  0.031939551  0.46982957  0.51656357
4 Cork       5.313609  0.083281515  1.43928884  2.24323856
5 Donegal    8.371808 -0.039371561 -1.39288713 -2.19776923
6 Dublin     5.443035 -0.010354512 -0.14127218 -0.14554367
7 Galway     4.520344  0.134873939  2.39189491  4.63522665
8 Kerry      8.144135  0.028431952  0.54051534  0.61545648
9 Kildare    3.169925  0.018723213  0.14926096  0.14688325
10 Kilkenny  4.120105  0.105365819  1.40668493  2.15214600
11 Laoghis   3.985449  0.001724096  0.01660985  0.01657177
12 Leitrim   3.547872  0.109608339  1.18229964  1.66578026
13 Limerick  5.347370  0.027585567  0.32820959  0.34241163
14 Longford  5.351218  0.108368224  2.22687206  4.19385821
15 Louth     8.096967  0.037745731  0.78968254  0.98878788
16 Mayo      4.684091  0.105317102  1.75922892  2.94711915
17 Meath     3.399289  0.020074178  0.15693992  0.15623206
18 Monaghan  6.422179  0.053418031  0.94193428  1.24723730
19 Offaly    3.401055  0.071432961  0.59871278  0.67858124
20 Roscommon 3.349691  0.357114199  4.33885200 10.02517077
21 Sligo     4.759210 -0.036185300 -0.60775394 -0.74635955
22 Tipperary 3.029041  0.006482570  0.04683010  0.04657633
23 Waterford 5.049095  0.093409563  1.61022194  2.62552879
24 Westmeath 4.596009  0.080097979  1.05978192  1.45704611
25 Wexford   4.921174  0.085478829  1.32647942  1.98902088
26 Wicklow   4.513581  0.020437514  0.21417067  0.21406975
> mean(e.locmor[,1])
[1] 0.3366057
> lm.morantest(e.lm, nb2listw(eire.nb))

	Global Moran's I for regression residuals

data:  
model: lm(formula = OWNCONS ~ ROADACC, data = eire.df)
weights: nb2listw(eire.nb)
 
Moran I statistic standard deviate = 3.2575, p-value = 0.0005619
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
        0.33660565        -0.05877741         0.01473183 

> hist(e.locmor[,"Pr. (Sad)"])
> e.wlm <- lm(OWNCONS ~ ROADACC, data=eire.df, weights=RETSALE)
> e.locmorw1 <- summary(localmoran.sad(e.wlm, eire.nb, select=1:nrow(eire.df), resfun=weighted.residuals))
> e.locmorw1
             Local Morans I Stand. dev. (N)      Pr. (N) Saddlepoint
1 Carlow        0.160490657      0.41009538 3.408680e-01   0.5772973
2 Cavan        -0.144663771     -0.27825575 6.095920e-01  -0.4530517
3 Clare         0.301676582      0.59021701 2.775226e-01   0.7898733
4 Cork          1.520488153      3.49016956 2.413571e-04   2.8366563
5 Donegal      -0.435899664     -0.44665946 6.724395e-01  -0.6713609
6 Dublin       -0.340222996     -0.60886675 7.286936e-01  -0.8565802
7 Galway        1.469009037      3.64546192 1.334560e-04   2.8227451
8 Kerry         0.268957279      0.49517211 3.102393e-01   0.6686101
9 Kildare       0.002996577      0.12659200 4.496317e-01   0.0997825
10 Kilkenny     0.497968801      1.20610829 1.138879e-01   1.3409138
11 Laoghis     -0.026328708     -0.01713904 5.068372e-01  -0.0651175
12 Leitrim      0.277306386      0.80644537 2.099930e-01   1.0117649
13 Limerick     0.263122939      0.67591893 2.495461e-01   0.8775963
14 Longford     0.605211711      1.23874274 1.077204e-01   1.3537585
15 Louth        0.359469683      0.53572990 2.960726e-01   0.7328019
16 Mayo         1.742480472      3.68118786 1.160749e-04   3.0150016
17 Meath       -0.112171618     -0.26680698 6.051911e-01  -0.4547053
18 Monaghan     0.241044892      0.46013751 3.227088e-01   0.6409416
19 Offaly       0.129191178      0.40988983 3.409434e-01   0.5720553
20 Roscommon    1.469671750      4.39927211 5.430728e-06   3.1321527
21 Sligo        0.095559559      0.31036587 3.781414e-01   0.3850306
22 Tipperary    0.088352646      0.39958273 3.447319e-01   0.5259210
23 Waterford    1.212658861      2.69846035 3.483052e-03   2.2929258
24 Westmeath    0.256165310      0.61222265 2.701952e-01   0.8162086
25 Wexford      0.619197906      1.31967483 9.347180e-02   1.4255383
26 Wicklow      0.006531073      0.13142161 4.477209e-01   0.1098672
               Pr. (Sad) Expectation   Variance   Skewness Kurtosis    Minimum
1 Carlow     0.281869320 -0.01840558 0.19029731 -0.1986977 6.709176  -5.665283
2 Cavan      0.674744237 -0.02184465 0.19482455 -0.2329761 6.717975  -5.769371
3 Clare      0.214800893 -0.02782578 0.31166901 -0.2346279 6.718435  -7.299407
4 Cork       0.002279433 -0.07147410 0.20805228 -0.7280203 7.002789  -6.495227
5 Donegal    0.749004675 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345
6 Dublin     0.804161523 -0.11187469 0.14065367 -1.3324828 7.767845  -5.846924
7 Galway     0.002380721 -0.04407925 0.17227545 -0.4973247 6.833103  -5.688263
8 Kerry      0.251872107 -0.05644300 0.43184063 -0.4031537 6.782459  -8.859407
9 Kildare    0.460258505 -0.04145378 0.12329287 -0.5519841 6.867423  -4.857131
10 Kilkenny  0.089974223 -0.02321457 0.18672759 -0.2528322 6.723714  -5.669156
11 Laoghis   0.525959778 -0.01882531 0.19166504 -0.2024943 6.710081  -5.689691
12 Leitrim   0.155825237 -0.03314655 0.14819776 -0.4041387 6.782933  -5.190860
13 Limerick  0.190081424 -0.04800976 0.21188592 -0.4885390 6.827925  -6.298874
14 Longford  0.087906718 -0.01321709 0.24923967 -0.1247567 6.694960  -6.392250
15 Louth     0.231839637 -0.02272663 0.50895713 -0.1500895 6.699098  -9.179410
16 Mayo      0.001284889 -0.09458039 0.24904116 -0.8745463 7.144787  -7.272523
17 Meath     0.675339370 -0.02548973 0.10555100 -0.3685280 6.766525  -4.353122
18 Monaghan  0.260780316 -0.02333303 0.33012248 -0.1912612 6.707452  -7.451275
19 Offaly    0.283642249 -0.01927989 0.13120470 -0.2505068 6.723017  -4.750083
20 Roscommon 0.000867648 -0.02385522 0.11525625 -0.3302939 6.750604  -4.517676
21 Sligo     0.350107359 -0.06927688 0.28207107 -0.6087587 6.906925  -7.416881
22 Tipperary 0.299471532 -0.03719246 0.09871568 -0.5534442 6.868390  -4.347214
23 Waterford 0.010926138 -0.04027429 0.21558757 -0.4070996 6.784366  -6.264083
24 Westmeath 0.207190421 -0.01522814 0.19650786 -0.1618342 6.701275  -5.716689
25 Wexford   0.077000826 -0.02786850 0.24041626 -0.2674357 6.728234  -6.450174
26 Wicklow   0.456257330 -0.04751424 0.16911517 -0.5404006 6.859847  -5.677417
              Maximum        omega       sad.r       sad.u
1 Carlow     5.223549  0.033637462  0.38794383  0.41751442
2 Cavan      5.245099 -0.022294725 -0.26091513 -0.27432856
3 Clare      6.631589  0.035302524  0.54866959  0.62630505
4 Cork       4.779848  0.134384022  2.56890121  5.11058941
5 Donegal    9.098033 -0.017507303 -0.40402088 -0.45010348
6 Dublin     3.161931 -0.040828131 -0.50710580 -0.60543071
7 Galway     4.630361  0.138454493  2.55314856  5.08170760
8 Kerry      7.504775  0.027195108  0.47167584  0.51758880
9 Kildare    3.862240  0.014230854  0.12280697  0.12246022
10 Kilkenny  5.112007  0.071351828  1.03314661  1.41988761
11 Laoghis   5.237883 -0.001502568 -0.01645549 -0.01646868
12 Leitrim   4.395343  0.066207108  0.74158109  0.90609823
13 Limerick  5.146640  0.050265468  0.63703133  0.74253221
14 Longford  6.075040  0.060534639  1.04112815  1.44165700
15 Louth     8.633971  0.025231866  0.49793592  0.55971045
16 Mayo      5.002594  0.135902733  2.75603129  5.62669411
17 Meath     3.741368 -0.028724497 -0.24912602 -0.26221742
18 Monaghan  6.891283  0.028042744  0.43280552  0.47360371
19 Offaly    4.287365  0.040883462  0.38909358  0.41780262
20 Roscommon 3.945151  0.180270100  2.87643937  6.00202551
21 Sligo     5.754236  0.023145822  0.30299868  0.31062426
22 Tipperary 3.454595  0.048932861  0.38768333  0.40902706
23 Waterford 5.297500  0.101874758  1.99944904  3.59542986
24 Westmeath 5.351214  0.044919886  0.56403221  0.65024353
25 Wexford   5.781330  0.066083430  1.11524637  1.57637406
26 Wicklow   4.537075  0.012609906  0.12748740  0.12720134
> e.locmorw2 <- summary(localmoran.sad(e.wlm, eire.nb, select=1:nrow(eire.df), resfun=rstudent))
> e.locmorw2
             Local Morans I Stand. dev. (N)      Pr. (N) Saddlepoint
1 Carlow        0.121997164      0.32185426 3.737816e-01  0.45871930
2 Cavan        -0.110588620     -0.20105599 5.796726e-01 -0.34808741
3 Clare         0.308759283      0.60290381 2.732863e-01  0.80379674
4 Cork          1.404203115      3.23522979 6.077244e-04  2.69598105
5 Donegal      -0.421182109     -0.42837428 6.658107e-01 -0.65187732
6 Dublin       -0.443534307     -0.88433550 8.117424e-01 -1.05167518
7 Galway        1.376190254      3.42183495 3.110003e-04  2.70663064
8 Kerry         0.241623387      0.45357724 3.250666e-01  0.61515126
9 Kildare       0.008842913      0.14324202 4.430495e-01  0.12690939
10 Kilkenny     0.382893124      0.93980330 1.736592e-01  1.12810394
11 Laoghis     -0.019904450     -0.00246494 5.009834e-01 -0.04176107
12 Leitrim      0.200483743      0.60688769 2.719627e-01  0.80241456
13 Limerick     0.238810092      0.62310059 2.666092e-01  0.81824678
14 Longford     0.466942853      0.96178354 1.680792e-01  1.14088225
15 Louth        0.271710988      0.41271732 3.399069e-01  0.58520655
16 Mayo         1.705850161      3.60778634 1.544103e-04  2.97346461
17 Meath       -0.160603054     -0.41587901 6.612507e-01 -0.63254531
18 Monaghan     0.181378604      0.35629110 3.608113e-01  0.50697175
19 Offaly       0.107919508      0.35116431 3.627325e-01  0.49312417
20 Roscommon    1.249826037      3.75170355 8.781854e-05  2.81402777
21 Sligo        0.079431883      0.27999953 3.897389e-01  0.33741411
22 Tipperary    0.085153638      0.38940098 3.484898e-01  0.51126046
23 Waterford    1.022922345      2.28982205 1.101582e-02  2.06385578
24 Westmeath    0.201539331      0.48899468 3.124227e-01  0.67791734
25 Wexford      0.481114325      1.03805702 1.496218e-01  1.21094348
26 Wicklow     -0.011694661      0.08710223 4.652951e-01  0.03786608
               Pr. (Sad) Expectation   Variance   Skewness Kurtosis    Minimum
1 Carlow     0.323217876 -0.01840558 0.19029731 -0.1986977 6.709176  -5.665283
2 Cavan      0.636112729 -0.02184465 0.19482455 -0.2329761 6.717975  -5.769371
3 Clare      0.210757187 -0.02782578 0.31166901 -0.2346279 6.718435  -7.299407
4 Cork       0.003509083 -0.07147410 0.20805228 -0.7280203 7.002789  -6.495227
5 Donegal    0.742759841 -0.07638800 0.64784767 -0.4450323 6.803659 -10.931345
6 Dublin     0.853525699 -0.11187469 0.14065367 -1.3324828 7.767845  -5.846924
7 Galway     0.003398492 -0.04407925 0.17227545 -0.4973247 6.833103  -5.688263
8 Kerry      0.269227417 -0.05644300 0.43184063 -0.4031537 6.782459  -8.859407
9 Kildare    0.449506058 -0.04145378 0.12329287 -0.5519841 6.867423  -4.857131
10 Kilkenny  0.129638014 -0.02321457 0.18672759 -0.2528322 6.723714  -5.669156
11 Laoghis   0.516655417 -0.01882531 0.19166504 -0.2024943 6.710081  -5.689691
12 Leitrim   0.211156597 -0.03314655 0.14819776 -0.4041387 6.782933  -5.190860
13 Limerick  0.206608144 -0.04800976 0.21188592 -0.4885390 6.827925  -6.298874
14 Longford  0.126959464 -0.01321709 0.24923967 -0.1247567 6.694960  -6.392250
15 Louth     0.279204420 -0.02272663 0.50895713 -0.1500895 6.699098  -9.179410
16 Mayo      0.001472292 -0.09458039 0.24904116 -0.8745463 7.144787  -7.272523
17 Meath     0.736484694 -0.02548973 0.10555100 -0.3685280 6.766525  -4.353122
18 Monaghan  0.306087322 -0.02333303 0.33012248 -0.1912612 6.707452  -7.451275
19 Offaly    0.310962427 -0.01927989 0.13120470 -0.2505068 6.723017  -4.750083
20 Roscommon 0.002446250 -0.02385522 0.11525625 -0.3302939 6.750604  -4.517676
21 Sligo     0.367902373 -0.06927688 0.28207107 -0.6087587 6.906925  -7.416881
22 Tipperary 0.304584343 -0.03719246 0.09871568 -0.5534442 6.868390  -4.347214
23 Waterford 0.019515696 -0.04027429 0.21558757 -0.4070996 6.784366  -6.264083
24 Westmeath 0.248912051 -0.01522814 0.19650786 -0.1618342 6.701275  -5.716689
25 Wexford   0.112958534 -0.02786850 0.24041626 -0.2674357 6.728234  -6.450174
26 Wicklow   0.484897230 -0.04751424 0.16911517 -0.5404006 6.859847  -5.677417
              Maximum         omega        sad.r        sad.u
1 Carlow     5.223549  0.0272472954  0.306852385  0.321490350
2 Cavan      5.245099 -0.0166242430 -0.190223798 -0.196022741
3 Clare      6.631589  0.0358559846  0.559584155  0.641527095
4 Cork       4.779848  0.1283688794  2.421993662  4.702934834
5 Donegal    9.098033 -0.0169574018 -0.388662370 -0.430528174
6 Dublin     3.161931 -0.0507848831 -0.696824139 -0.892299501
7 Galway     4.630361  0.1333224875  2.431707338  4.745166958
8 Kerry      7.504775  0.0252982005  0.433626352  0.469138111
9 Kildare    3.862240  0.0161278548  0.139072871  0.138837812
10 Kilkenny  5.112007  0.0622219791  0.835166590  1.066654825
11 Laoghis   5.237883 -0.0002164925 -0.002368023 -0.002368244
12 Leitrim   4.395343  0.0543844388  0.571625643  0.652237768
13 Limerick  5.146640  0.0473787285  0.590605630  0.675595582
14 Longford  6.075040  0.0528365356  0.840671447  1.082014178
15 Louth     8.633971  0.0204960239  0.389078238  0.419930705
16 Mayo      5.002594  0.1340509166  2.712635049  5.503894365
17 Meath     3.741368 -0.0415411327 -0.379736494 -0.417998694
18 Monaghan  6.891283  0.0226076552  0.338579266  0.358443998
19 Offaly    4.287365  0.0357600182  0.335019324  0.353243066
20 Roscommon 3.945151  0.1623235556  2.543240406  5.063795948
21 Sligo     5.754236  0.0209568244  0.273376649  0.278204612
22 Tipperary 3.454595  0.0478130890  0.377982061  0.397511387
23 Waterford 5.297500  0.0941811771  1.762051071  2.998984773
24 Westmeath 5.351214  0.0379323563  0.457473561  0.506014991
25 Wexford   5.781330  0.0582538352  0.911459483  1.197527949
26 Wicklow   4.537075  0.0083101099  0.084281843  0.083952776
> e.errorsar <- errorsarlm(OWNCONS ~ ROADACC, data=eire.df,
+  listw=nb2listw(eire.nb))
> e.errorsar

Call:
errorsarlm(formula = OWNCONS ~ ROADACC, data = eire.df, listw = nb2listw(eire.nb))
Type: error 

Coefficients:
(Intercept)     ROADACC      lambda 
2.892719569 0.002800913 0.783970989 

Log likelihood: -64.12465 
> e.clocmor <- summary(localmoran.sad(e.errorsar, eire.nb, select=1:nrow(eire.df)))
> e.clocmor
             Local Morans I Stand. dev. (N)     Pr. (N) Saddlepoint   Pr. (Sad)
1 Carlow        0.216996683     -0.23901926 0.594454678  0.23886184 0.405606359
2 Cavan        -0.372573613     -0.86382085 0.806156844 -1.57032046 0.941829712
3 Clare         0.231975105     -0.39573770 0.653850731 -0.01412279 0.505633989
4 Cork          0.781935479     -0.04503638 0.517960846  0.46824506 0.319804675
5 Donegal      -1.690640590     -1.45417673 0.927051342 -2.07884411 0.981184159
6 Dublin       -0.160696921     -0.66719838 0.747677287 -0.99638658 0.840468826
7 Galway        1.313714727      1.64460273 0.050025882  1.78369879 0.037236311
8 Kerry         0.365348659     -0.48706410 0.686893548 -0.15063115 0.559866657
9 Kildare      -0.025575445     -0.48237140 0.685228933 -0.50743626 0.694075627
10 Kilkenny     0.576843308      0.36104345 0.359033484  0.82525579 0.204613193
11 Laoghis     -0.059517978     -0.50300377 0.692519190 -0.64162073 0.739440265
12 Leitrim      0.384845866      0.12735264 0.449330650  0.61582501 0.269005011
13 Limerick     0.118179867     -0.57236200 0.716461624 -0.41657602 0.661505725
14 Longford     1.416432004      1.08802782 0.138291413  1.28377211 0.099610852
15 Louth        0.562429203     -0.32854059 0.628748522  0.16627427 0.433970556
16 Mayo         0.875727038      1.01197955 0.155773915  1.33880356 0.090317316
17 Meath        0.003678560     -0.59077624 0.722664823 -0.58846521 0.721889960
18 Monaghan     0.550983111     -0.26861659 0.605887626  0.22679194 0.410292764
19 Offaly       0.151555560     -0.01296477 0.505172052  0.44669970 0.327545950
20 Roscommon    2.043688390      2.37913310 0.008676704  3.05159819 0.001138133
21 Sligo       -0.475798710     -1.04286177 0.851493842 -1.67839510 0.953365003
22 Tipperary   -0.034541063     -0.60752056 0.728247248 -0.70912655 0.760877025
23 Waterford    0.857234228      0.59180803 0.276989574  0.98420674 0.162506935
24 Westmeath    0.451385718     -0.01202248 0.504796158  0.49676990 0.309675660
25 Wexford      0.643718339      0.21239755 0.415898450  0.70960108 0.238975775
26 Wicklow      0.024419502     -0.51385193 0.696322241 -0.40364018 0.656761333
             Expectation  Variance   Skewness  Kurtosis    Minimum   Maximum
1 Carlow      0.41510574 0.6869780  2.0117855  9.261988  -4.206946 14.169483
2 Cavan       0.84086832 1.9732887  2.2256282  9.916278  -4.555439 24.736279
3 Clare       0.78560219 1.9571306  2.1550023  9.687085  -5.534252 24.388704
4 Cork        0.85119474 2.3649862  2.1379028  9.633700  -6.317437 26.746111
5 Donegal     0.76633183 2.8547375  1.8788004  8.907007  -9.982656 28.374620
6 Dublin      0.53670402 1.0925846  2.0442431  9.354160  -5.066960 17.947857
7 Galway     -0.16789312 0.8116046 -0.8605749  7.130082 -13.100271  9.070836
8 Kerry       1.64399605 6.8917473  2.2694519 10.066471  -7.074158 46.530063
9 Kildare     0.26242834 0.3564785  1.8360154  8.800025  -3.671416  9.969696
10 Kilkenny   0.28971957 0.6324399  1.5830238  8.231934  -5.881831 12.835101
11 Laoghis    0.23336759 0.3390420  1.7104386  8.504746  -3.959897  9.560720
12 Leitrim    0.29318752 0.5179980  1.7324831  8.554628  -4.816083 11.852584
13 Limerick   1.23120165 3.7815142  2.2791638 10.100716  -4.969517 34.518356
14 Longford   0.18291084 1.2853258  0.7489112  7.021392 -11.808447 16.198307
15 Louth      1.23755546 4.2227164  2.2318508  9.937200  -6.517068 36.218399
16 Mayo      -0.04068769 0.8200506 -0.2115638  6.712314 -11.789109 10.812605
17 Meath      0.61648461 1.0759697  2.2181654  9.891351  -3.450422 18.246052
18 Monaghan   1.02287751 3.0861995  2.1961065  9.818688  -6.254862 30.803922
19 Offaly     0.15762584 0.2192235  1.4810040  8.031758  -3.668995  7.452015
20 Roscommon -0.63756938 1.2701051 -2.1636161  9.714273 -19.670778  4.369113
21 Sligo      0.36523619 0.6503910  1.8767733  8.901862  -4.774269 13.539937
22 Tipperary  0.48448255 0.7298814  2.1663926  9.723080  -3.289946 14.917527
23 Waterford  0.30429863 0.8729460  1.4393522  7.954516  -7.482000 14.785167
24 Westmeath  0.46292085 0.9205712  1.9622842  9.125722  -5.183761 16.293861
25 Wexford    0.42990119 1.0134121  1.7966973  8.704629  -6.403915 16.721543
26 Wicklow    0.52006242 0.9303831  2.1060292  9.536196  -4.220532 16.702030
                    omega       sad.r       sad.u
1 Carlow     -0.006183657 -0.11988414 -0.11483747
2 Cavan      -0.076730577 -1.41580886 -1.76201827
3 Clare      -0.014488539 -0.37297689 -0.32625268
4 Cork        0.001664894  0.07041289  0.07241322
5 Donegal    -0.039916017 -1.82964925 -2.88655418
6 Dublin     -0.054218890 -0.92650741 -0.98847724
7 Galway      0.041810060  1.49306772  2.30427191
8 Kerry      -0.013781253 -0.54171950 -0.43829323
9 Kildare    -0.050569403 -0.56760272 -0.54854597
10 Kilkenny   0.016666016  0.46992951  0.55532915
11 Laoghis   -0.052988992 -0.61500273 -0.62515327
12 Leitrim    0.011430634  0.25376401  0.27818400
13 Limerick  -0.031417774 -0.74232781 -0.58287708
14 Longford   0.019745434  0.95318659  1.30625607
15 Louth     -0.005622564 -0.23971180 -0.21748235
16 Mayo       0.030356932  1.04352038  1.42010951
17 Meath     -0.057912215 -0.78252590 -0.67227636
18 Monaghan  -0.004511205 -0.17504333 -0.16315407
19 Offaly     0.009772617  0.12658074  0.13181524
20 Roscommon  0.100863019  2.82165667  5.39860295
21 Sligo     -0.076577219 -1.44263443 -2.02706181
22 Tipperary -0.068249867 -0.81232359 -0.74700313
23 Waterford  0.017479859  0.63251438  0.79009519
24 Westmeath  0.004353521  0.11813859  0.12354302
25 Wexford    0.010304716  0.34491868  0.39115131
26 Wicklow   -0.039529611 -0.60645910 -0.53626901
> hist(e.clocmor[,"Pr. (Sad)"])
> 
> 
> 
> cleanEx(); ..nameEx <- "mat2listw"
> 
> ### * mat2listw
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: mat2listw
> ### Title: Convert a square spatial weights matrix to a weights list object
> ### Aliases: mat2listw
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> col005 <- dnearneigh(coords, 0, 0.5, attr(col.gal.nb, "region.id"))
> summary(col005)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 170 
Percentage nonzero weights: 7.080383 
Average number of links: 3.469388 
4 regions with no links:
1005 1006 1008 1043
Link number distribution:

 0  1  2  3  4  5  6  7  8  9 
 4 11  5  8  3  9  2  2  3  2 
11 least connected regions:
1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link
2 most connected regions:
1038 1036 with 9 links
> col005.w.mat <- nb2mat(col005, zero.policy=TRUE)
> col005.w.b <- mat2listw(col005.w.mat)
> summary(col005.w.b$neighbours)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 170 
Percentage nonzero weights: 7.080383 
Average number of links: 3.469388 
4 regions with no links:
1005 1006 1008 1043
Link number distribution:

 0  1  2  3  4  5  6  7  8  9 
 4 11  5  8  3  9  2  2  3  2 
11 least connected regions:
1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link
2 most connected regions:
1038 1036 with 9 links
> diffnb(col005, col005.w.b$neighbours)
> 
> 
> 
> cleanEx(); ..nameEx <- "moran"
> 
> ### * moran
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: moran
> ### Title: Compute Moran's I
> ### Aliases: moran
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> col.W <- nb2listw(COL.nb, style="W")
> crime <- spNamedVec("CRIME", COL.OLD)
> str(moran(crime, col.W, length(COL.nb), Szero(col.W)))
List of 2
 $ I: num 0.511
 $ K: num 2.23
> is.na(crime) <- sample(1:length(crime), 10)
> str(moran(crime, col.W, length(COL.nb), Szero(col.W), NAOK=TRUE))
List of 2
 $ I: num 0.468
 $ K: num 2.65
> 
> 
> 
> cleanEx(); ..nameEx <- "moran.mc"
> 
> ### * moran.mc
> 
> flush(stderr()); flush(stdout())
> 
> ### Encoding: latin1
> 
> ### Name: moran.mc
> ### Title: Permutation test for Moran's I statistic
> ### Aliases: moran.mc
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> colw <- nb2listw(COL.nb, style="W")
> nsim <- 99
> set.seed(1234)
> sim1 <- moran.mc(spNamedVec("CRIME", COL.OLD), listw=colw, nsim=nsim)
> sim1

	Monte-Carlo simulation of Moran's I

data:  spNamedVec("CRIME", COL.OLD) 
weights: colw  
number of simulations + 1: 100 
 
statistic = 0.511, observed rank = 100, p-value = 0.01
alternative hypothesis: greater 

> mean(sim1$res[1:nsim])
[1] -0.01735822
> var(sim1$res[1:nsim])
[1] 0.008938155
> summary(sim1$res[1:nsim])
     Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
-0.238200 -0.083270 -0.007406 -0.017360  0.039720  0.259400 
> MoranI.boot <- function(var, i, ...) {
+ var <- var[i]
+ return(moran(x=var, ...)$I)
+ }
> set.seed(1234)
> library(boot)
> boot1 <- boot(spNamedVec("CRIME", COL.OLD), statistic=MoranI.boot, R=nsim, sim="permutation", listw=colw, n=nrow(COL.OLD), S0=Szero(colw))
> boot1

DATA PERMUTATION


Call:
boot(data = spNamedVec("CRIME", COL.OLD), statistic = MoranI.boot, 
    R = nsim, sim = "permutation", listw = colw, n = nrow(COL.OLD), 
    S0 = Szero(colw))


Bootstrap Statistics :
     original     bias    std. error
t1* 0.5109513 -0.5283095  0.09454181
> plot(boot1)
> mean(boot1$t)
[1] -0.01735822
> var(boot1$t)
            [,1]
[1,] 0.008938155
> summary(boot1$t)
     object         
 Min.   :-0.238206  
 1st Qu.:-0.083268  
 Median :-0.007406  
 Mean   :-0.017358  
 3rd Qu.: 0.039717  
 Max.   : 0.259444  
> colold.lags <- nblag(COL.nb, 3)
> set.seed(1234)
> sim2 <- moran.mc(spNamedVec("CRIME", COL.OLD), nb2listw(colold.lags[[2]],
+  style="W"), nsim=nsim)
> summary(sim2$res[1:nsim])
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-0.18440 -0.06090 -0.01837 -0.01522  0.02860  0.23550 
> sim3 <- moran.mc(spNamedVec("CRIME", COL.OLD), nb2listw(colold.lags[[3]],
+  style="W"), nsim=nsim)
> summary(sim3$res[1:nsim])
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-0.16810 -0.06701 -0.02035 -0.01733  0.02200  0.14340 
> 
> 
> 
> cleanEx(); ..nameEx <- "moran.plot"
> 
> ### * moran.plot
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: moran.plot
> ### Title: Moran scatterplot
> ### Aliases: moran.plot
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(afcon)
> moran.plot(spNamedVec("totcon", afcon), nb2listw(paper.nb),
+  labels=as.character(afcon$name), pch=19)
Potentially influential observations of
	 lm(formula = wx ~ x) :

         dfb.1_ dfb.x dffit cov.r   cook.d hat    
EGYPT    -0.33   0.56  0.59  1.48_*  0.17   0.32_*
SUDAN     0.29  -0.51 -0.53  1.34_*  0.14   0.25_*
ETHIOPIA  0.10   0.18  0.41  0.83_*  0.08   0.03  
RWANDA    0.45  -0.28  0.46  0.85_*  0.10   0.04  
> moran.plot(scale(spNamedVec("totcon", afcon)), nb2listw(paper.nb),
+  labels=as.character(afcon$name), xlim=c(-2, 4), ylim=c(-2,4), pch=19)
Potentially influential observations of
	 lm(formula = wx ~ x) :

         dfb.1_ dfb.x dffit cov.r   cook.d hat    
EGYPT     0.16   0.56  0.59  1.48_*  0.17   0.32_*
SUDAN    -0.17  -0.51 -0.53  1.34_*  0.14   0.25_*
ETHIOPIA  0.37   0.18  0.41  0.83_*  0.08   0.03  
RWANDA    0.36  -0.28  0.46  0.85_*  0.10   0.04  
> 
> 
> 
> cleanEx(); ..nameEx <- "moran.test"
> 
> ### * moran.test
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: moran.test
> ### Title: Moran's I test for spatial autocorrelation
> ### Aliases: moran.test
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb, style="W"))

	Moran's I test under randomisation

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(COL.nb, style = "W")  
 
Moran I statistic standard deviate = 5.6341, p-value = 8.797e-09
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.510951264      -0.020833333       0.008908762 

> moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb, style="B"))

	Moran's I test under randomisation

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(COL.nb, style = "B")  
 
Moran I statistic standard deviate = 6.2116, p-value = 2.622e-10
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
       0.52063815       -0.02083333        0.00759872 

> moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb, style="C"))

	Moran's I test under randomisation

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(COL.nb, style = "C")  
 
Moran I statistic standard deviate = 6.2116, p-value = 2.622e-10
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
       0.52063815       -0.02083333        0.00759872 

> moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb, style="S"))

	Moran's I test under randomisation

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(COL.nb, style = "S")  
 
Moran I statistic standard deviate = 5.9786, p-value = 1.125e-09
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.512957470      -0.020833333       0.007971504 

> moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb, style="W"),
+  randomisation=FALSE)

	Moran's I test under normality

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(COL.nb, style = "W")  
 
Moran I statistic standard deviate = 5.6754, p-value = 6.92e-09
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.510951264      -0.020833333       0.008779831 

> colold.lags <- nblag(COL.nb, 3)
> moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(colold.lags[[2]],
+  style="W"))

	Moran's I test under randomisation

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(colold.lags[[2]], style = "W")  
 
Moran I statistic standard deviate = 2.6076, p-value = 0.004559
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.168485742      -0.020833333       0.005271314 

> moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(colold.lags[[3]],
+  style="W"))

	Moran's I test under randomisation

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(colold.lags[[3]], style = "W")  
 
Moran I statistic standard deviate = -1.7896, p-value = 0.9632
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
     -0.138930745      -0.020833333       0.004354683 

> print(is.symmetric.nb(COL.nb))
[1] TRUE
> COL.k4.nb <- knn2nb(knearneigh(coords.OLD, 4))
> print(is.symmetric.nb(COL.k4.nb))
Non-symmetric neighbours list
[1] FALSE
> moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.k4.nb, style="W"))

	Moran's I test under randomisation

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(COL.k4.nb, style = "W")  
 
Moran I statistic standard deviate = 6.734, p-value = 8.254e-12
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.582551727      -0.020833333       0.008028696 

> moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.k4.nb, style="W"),
+  randomisation=FALSE)

	Moran's I test under normality

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(COL.k4.nb, style = "W")  
 
Moran I statistic standard deviate = 6.7859, p-value = 5.767e-12
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.582551727      -0.020833333       0.007906215 

> cat("Note: non-symmetric weights matrix, use listw2U()")
Note: non-symmetric weights matrix, use listw2U()> moran.test(spNamedVec("CRIME", COL.OLD), listw2U(nb2listw(COL.k4.nb,
+  style="W")))

	Moran's I test under randomisation

data:  spNamedVec("CRIME", COL.OLD)  
weights: listw2U(nb2listw(COL.k4.nb, style = "W"))  
 
Moran I statistic standard deviate = 6.6554, p-value = 1.412e-11
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.582551727      -0.020833333       0.008219304 

> moran.test(spNamedVec("CRIME", COL.OLD), listw2U(nb2listw(COL.k4.nb,
+  style="W")), randomisation=FALSE)

	Moran's I test under normality

data:  spNamedVec("CRIME", COL.OLD)  
weights: listw2U(nb2listw(COL.k4.nb, style = "W"))  
 
Moran I statistic standard deviate = 6.7042, p-value = 1.013e-11
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.582551727      -0.020833333       0.008100198 

> ranks <- rank(COL.OLD$CRIME)
> names(ranks) <- rownames(COL.OLD)
> moran.test(ranks, nb2listw(COL.nb, style="W"), rank=TRUE)

	Moran's I test under randomisation

data:  ranks using rank correction 
weights: nb2listw(COL.nb, style = "W")  
 
Moran I statistic standard deviate = 6.3815, p-value = 8.766e-11
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.584333495      -0.020833333       0.008992923 

> crime <- spNamedVec("CRIME", COL.OLD)
> is.na(crime) <- sample(1:length(crime), 10)
> res <- try(moran.test(crime, nb2listw(COL.nb, style="W"), na.action=na.fail))
Error in na.fail.default(x) : missing values in object
> res
[1] "Error in na.fail.default(x) : missing values in object\n"
attr(,"class")
[1] "try-error"
> moran.test(crime, nb2listw(COL.nb, style="W"), zero.policy=TRUE,
+  na.action=na.omit)

	Moran's I test under randomisation

data:  crime  
weights: nb2listw(COL.nb, style = "W") 
omitted: 3, 10, 14, 18, 26, 27, 28, 40, 41, 42 
 
Moran I statistic standard deviate = 4.3361, p-value = 7.252e-06
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
       0.48158092       -0.02631579        0.01372000 

> moran.test(crime, nb2listw(COL.nb, style="W"), zero.policy=TRUE,
+  na.action=na.exclude)

	Moran's I test under randomisation

data:  crime  
weights: nb2listw(COL.nb, style = "W") 
omitted: 3, 10, 14, 18, 26, 27, 28, 40, 41, 42 
 
Moran I statistic standard deviate = 4.3361, p-value = 7.252e-06
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
       0.48158092       -0.02631579        0.01372000 

> moran.test(crime, nb2listw(COL.nb, style="W"), na.action=na.pass)

	Moran's I test under randomisation

data:  crime  
weights: nb2listw(COL.nb, style = "W")  
 
Moran I statistic standard deviate = 5.2041, p-value = 9.745e-08
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.468028838      -0.020833333       0.008824189 

> 
> 
> 
> cleanEx(); ..nameEx <- "nb2blocknb"
> 
> ### * nb2blocknb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nb2blocknb
> ### Title: Block up neighbour list for location-less observations
> ### Aliases: nb2blocknb
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(boston)
> summary(as.vector(table(boston.c$TOWN)))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
    1.0     2.0     4.0     5.5     7.0    30.0 
> townaggr <- aggregate(boston.utm, list(town=boston.c$TOWN), mean)
> block.rel <- graph2nb(relativeneigh(as.matrix(townaggr[,2:3])), as.character(townaggr[,1]), sym=TRUE)
> block.rel
Neighbour list object:
Number of regions: 92 
Number of nonzero links: 240 
Percentage nonzero weights: 2.835539 
Average number of links: 2.608696 
> print(is.symmetric.nb(block.rel))
[1] TRUE
> plot(block.rel, as.matrix(townaggr[,2:3]))
> points(boston.utm, pch=18, col="lightgreen")
> block.nb <- nb2blocknb(block.rel, as.character(boston.c$TOWN))
> block.nb
Neighbour list object:
Number of regions: 506 
Number of nonzero links: 15234 
Percentage nonzero weights: 5.949945 
Average number of links: 30.10672 
> print(is.symmetric.nb(block.nb))
[1] TRUE
> plot(block.nb, boston.utm)
> points(boston.utm, pch=18, col="lightgreen")
> moran.test(boston.c$CMEDV, nb2listw(boston.soi))

	Moran's I test under randomisation

data:  boston.c$CMEDV  
weights: nb2listw(boston.soi)  
 
Moran I statistic standard deviate = 21.7861, p-value < 2.2e-16
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.690285059      -0.001980198       0.001009685 

> moran.test(boston.c$CMEDV, nb2listw(block.nb))

	Moran's I test under randomisation

data:  boston.c$CMEDV  
weights: nb2listw(block.nb)  
 
Moran I statistic standard deviate = 22.4546, p-value < 2.2e-16
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
     0.3122905961     -0.0019801980      0.0001958827 

> 
> 
> 
> cleanEx(); ..nameEx <- "nb2lines"
> 
> ### * nb2lines
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nb2lines
> ### Title: Use arc-type shapefiles for import and export of weights
> ### Aliases: nb2lines listw2lines df2sn
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> res <- listw2lines(nb2listw(col.gal.nb), coords)
> str(res$df)
`data.frame':	230 obs. of  5 variables:
 $ i   : int  1 1 2 2 2 3 3 3 3 4 ...
 $ j   : int  2 3 1 3 4 1 2 4 5 2 ...
 $ i_ID:Class 'AsIs'  chr [1:230] "1005" "1005" "1001" "1001" ...
 $ j_ID:Class 'AsIs'  chr [1:230] "1001" "1006" "1005" "1006" ...
 $ wt  : num  0.500 0.500 0.333 0.333 0.333 ...
> fn <- paste(tempdir(), "nbshape", sep="/")
> write.linelistShape(res$ll, res$df, file=fn)
> inMap <- read.shape(fn)
Shapefile Type: Line   # of Shapes: 230 
> str(inMap$att.data)
`data.frame':	230 obs. of  5 variables:
 $ i   : int  1 1 2 2 2 3 3 3 3 4 ...
 $ j   : int  2 3 1 3 4 1 2 4 5 2 ...
 $ i_ID: Factor w/ 49 levels "1001","1002",..: 5 5 1 1 1 6 6 6 6 2 ...
 $ j_ID: Factor w/ 49 levels "1001","1002",..: 1 6 5 6 2 5 1 2 7 1 ...
 $ wt  : num  0.500 0.500 0.333 0.333 0.333 ...
 - attr(*, "data_types")= chr  "N" "N" "C" "C" ...
> diffnb(sn2listw(df2sn(inMap$att.data))$neighbours, col.gal.nb)
> identical(coords, unique(t(sapply(Map2lines(inMap), function(x) x[1,]))))
[1] TRUE
> 
> 
> 
> cleanEx(); ..nameEx <- "nb2listw"
> 
> ### * nb2listw
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nb2listw
> ### Title: Spatial weights for neighbours lists
> ### Aliases: nb2listw
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> cards <- card(col.gal.nb)
> col.w <- nb2listw(col.gal.nb)
> plot(cards, unlist(lapply(col.w$weights, sum)),xlim=c(0,10),
+ ylim=c(0,10), xlab="number of links", ylab="row sums of weights")
> col.b <- nb2listw(col.gal.nb, style="B")
> points(cards, unlist(lapply(col.b$weights, sum)), col="red")
> col.c <- nb2listw(col.gal.nb, style="C")
> points(cards, unlist(lapply(col.c$weights, sum)), col="green")
> col.u <- nb2listw(col.gal.nb, style="U")
> points(cards, unlist(lapply(col.u$weights, sum)), col="orange")
> col.s <- nb2listw(col.gal.nb, style="S")
> points(cards, unlist(lapply(col.s$weights, sum)), col="blue")
> legend(x=c(0, 1), y=c(7, 9), legend=c("W", "B", "C", "U", "S"),
+ col=c("black", "red", "green", "orange", "blue"), pch=rep(1,5))
> dlist <- nbdists(col.gal.nb, coords)
> dlist <- lapply(dlist, function(x) 1/x)
> col.w.d <- nb2listw(col.gal.nb, glist=dlist)
> summary(unlist(col.w$weights))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.1000  0.1429  0.1667  0.2130  0.2500  0.5000 
> summary(unlist(col.w.d$weights))
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
0.06977 0.13110 0.17710 0.21300 0.27120 0.67180 
> 
> 
> 
> cleanEx(); ..nameEx <- "nb2mat"
> 
> ### * nb2mat
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nb2mat
> ### Title: Spatial weights matrices for neighbours lists
> ### Aliases: nb2mat listw2mat
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> col005 <- dnearneigh(coords, 0, 0.5, attr(col.gal.nb, "region.id"))
> summary(col005)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 170 
Percentage nonzero weights: 7.080383 
Average number of links: 3.469388 
4 regions with no links:
1005 1006 1008 1043
Link number distribution:

 0  1  2  3  4  5  6  7  8  9 
 4 11  5  8  3  9  2  2  3  2 
11 least connected regions:
1001 1007 1018 1010 1045 1044 1046 1047 1049 1048 1015 with 1 link
2 most connected regions:
1038 1036 with 9 links
> col005.w.mat <- nb2mat(col005, zero.policy=TRUE)
> table(round(apply(col005.w.mat, 1, sum)))

 0  1 
 4 45 
> 
> 
> 
> cleanEx(); ..nameEx <- "nbdists"
> 
> ### * nbdists
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nbdists
> ### Title: Spatial link distance measures
> ### Aliases: nbdists
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> dlist <- nbdists(col.gal.nb, coords)
> dlist <- lapply(dlist, function(x) 1/x)
> stem(unlist(dlist))

  The decimal point is at the |

  1 | 1111112222223333334444444444
  1 | 555555556666667777777777888888888899999999999999999999
  2 | 00000000111111111111111122222222222222333333333333334444
  2 | 55555555556666666666666677777777888888999999
  3 | 0000111111222233334444
  3 | 77779999
  4 | 223344
  4 | 77
  5 | 001144
  5 | 
  6 | 
  6 | 99
  7 | 
  7 | 88

> 
> 
> 
> cleanEx(); ..nameEx <- "nblag"
> 
> ### * nblag
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nblag
> ### Title: Higher order neighbours lists
> ### Aliases: nblag
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> summary(col.gal.nb, coords)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 230 
Percentage nonzero weights: 9.579342 
Average number of links: 4.693878 
Link number distribution:

 2  3  4  5  6  7  8  9 10 
 7  7 13  4  9  6  1  1  1 
7 least connected regions:
1005 1008 1045 1047 1049 1048 1015 with 2 links
1 most connected region:
1017 with 10 links
Summary of link distances:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.1276  0.3613  0.4566  0.4694  0.5536  0.8924 

  The decimal point is 1 digit(s) to the left of the |

  1 | 3344
  1 | 99
  2 | 000011333344
  2 | 556677779999
  3 | 000011222222223344444444
  3 | 556666777777888888889999999999
  4 | 00001111112233333333334444
  4 | 55666666666666777777777788888899
  5 | 0011112222222222222233334444
  5 | 556666667788
  6 | 000000112244
  6 | 5577889999
  7 | 11112244
  7 | 557777
  8 | 1144
  8 | 55999999

> library(maptools)
> plot(polys, border="grey", forcefill=FALSE)
> plot(col.gal.nb, coords, add=TRUE)
> title(main="GAL order 1 (black) and 2 (red) links")
> col.lags <- nblag(col.gal.nb, 2)
> summary(col.lags[[2]], coords)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 406 
Percentage nonzero weights: 16.90962 
Average number of links: 8.285714 
Link number distribution:

 1  2  3  4  5  6  7  8  9 10 11 12 13 14 15 16 17 
 1  2  5  4  2  3  5  4  2  3  7  3  4  1  1  1  1 
1 least connected region:
1046 with 1 link
1 most connected region:
1032 with 17 links
Summary of link distances:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.3209  0.7126  0.8481  0.9023  1.0860  1.6740 

  The decimal point is 1 digit(s) to the left of the |

   3 | 2233557799
   4 | 1166777788888888
   5 | 0011224455555566666688889999
   6 | 11113333334455556666666666889999999999
   7 | 00000011112222222233334444444455555555556666667777777777777777889999
   8 | 000011111111222222222233333344444444445555555555666666999999
   9 | 001111222222222233444444555555556666667777778899
  10 | 0000002222223333333344666666777788889999
  11 | 00112233334444555566777788
  12 | 1122223333555566667777888888889999
  13 | 0000001166668899
  14 | 002244558888
  15 | 00667788
  16 | 77

> plot(col.lags[[2]], coords, add=TRUE, col="red", lty=2)
> 
> 
> 
> cleanEx(); ..nameEx <- "nboperations"
> 
> ### * nboperations
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nb.set.operations
> ### Title: Set operations on neighborhood objects
> ### Aliases: intersect.nb union.nb setdiff.nb complement.nb
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> col.tri.nb <- tri2nb(coords)
> oldpar <- par(mfrow=c(1,2))
> col.soi.nb <- graph2nb(soi.graph(col.tri.nb, coords))
> library(maptools)
> plot(polys, border="grey", forcefill=FALSE)
> plot(col.soi.nb, coords, add=TRUE)
> title(main="Sphere of Influence Graph")
> plot(polys, border="grey", forcefill=FALSE)
> plot(complement.nb(col.soi.nb), coords, add=TRUE)
> title(main="Complement of Sphere of Influence Graph")
> par(mfrow=c(2,2))
> col2 <- droplinks(col.gal.nb, 21)
> plot(intersect.nb(col.gal.nb, col2), coords)
> title(main="Intersect")
> plot(union.nb(col.gal.nb, col2), coords)
> title(main="Union")
> plot(setdiff.nb(col.gal.nb, col2), coords)
> title(main="Set diff")
> par(oldpar)
> 
> 
> 
> graphics::par(get("par.postscript", env = .CheckExEnv))
> cleanEx(); ..nameEx <- "nc.sids"
> 
> ### * nc.sids
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: nc.sids
> ### Title: North Carolina SIDS data
> ### Aliases: nc.sids ncCR85.nb ncCC89.nb sidspolys sidscents
> ### Keywords: datasets
> 
> ### ** Examples
> 
> library(maptools)
> data(nc.sids)
> plot(sidspolys, border="grey", forcefill=FALSE)
> plot(ncCR85.nb, sidscents, add=TRUE, col="blue")
> plot(sidspolys, border="grey", forcefill=FALSE)
> plot(ncCC89.nb, cbind(nc.sids$lon, nc.sids$lat),
+  add=TRUE, col="blue")
> 
> 
> 
> cleanEx(); ..nameEx <- "p.adjustSP"
> 
> ### * p.adjustSP
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: p.adjustSP
> ### Title: Adjust local association measures' p-values
> ### Aliases: p.adjustSP
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(afcon)
> oid <- order(afcon$id)
> resG <- as.vector(localG(spNamedVec("totcon", afcon), nb2listw(include.self(paper.nb))))
> non <- format.pval(pnorm(2*(abs(resG)), lower.tail=FALSE), 2)
> bon <- format.pval(p.adjustSP(pnorm(2*(abs(resG)), lower.tail=FALSE), paper.nb, "bonferroni"), 2)
> tot <- format.pval(p.adjust(pnorm(2*(abs(resG)), lower.tail=FALSE), "bonferroni", n=length(resG)), 2)
> data.frame(resG, non, bon, tot, row.names=afcon$name)[oid,]
                                resG     non     bon     tot
THE GAMBIA               -0.98383592 0.02455 0.04911  1.0000
MALI                     -1.69893391 0.00034 0.00272  0.0143
SENEGAL                  -1.46321911 0.00171 0.00857  0.0720
BENIN                    -1.30139679 0.00462 0.02312  0.1942
MAURITANIA               -0.60496775 0.11315 0.56576  1.0000
NIGER                    -1.04877003 0.01797 0.14378  0.7549
IVORY COAST              -1.41712454 0.00230 0.01378  0.0965
GUINEA                   -1.44888005 0.00188 0.01128  0.0789
BURKINA FASO             -1.75085492 0.00023 0.00162  0.0097
LIBERIA                  -1.04053617 0.01871 0.07485  0.7860
SIERRA LEONE             -0.87032623 0.04087 0.12262  1.0000
GHANA                    -1.10269327 0.01371 0.05485  0.5760
TOGO                     -0.99053008 0.02379 0.09517  0.9993
CAMEROON                 -1.13328519 0.01171 0.07025  0.4917
NIGERIA                  -1.17261672 0.00951 0.04754  0.3993
GABON                    -0.78935857 0.05720 0.17160  1.0000
CENTRAL AFRICAN REPUBLIC  1.17349763 0.00946 0.05678  0.3974
CHAD                      0.46259185 0.17744 1.00000  1.0000
CONGO                    -0.20253005 0.34272 1.00000  1.0000
ZAIRE                     2.02270432 2.6e-05 0.00026  0.0011
ANGOLA                    1.23450728 0.00677 0.02710  0.2845
UGANDA                    3.33600851 1.3e-11 7.6e-11 5.3e-10
KENYA                     3.50301896 1.2e-12 7.4e-12 5.1e-11
TANZANIA                  1.09843592 0.01401 0.12613  0.5886
BURUNDI                   0.77417084 0.06077 0.24308  1.0000
RWANDA                    1.45720776 0.00178 0.00891  0.0748
SOMALIA                   1.18316273 0.00898 0.02695  0.3773
ETHIOPIA                  2.62720027 7.4e-08 3.0e-07 3.1e-06
ZAMBIA                    0.75273285 0.06610 0.59492  1.0000
ZIMBABWE                 -0.19956472 0.34490 1.00000  1.0000
MALAWI                    0.21195283 0.33582 1.00000  1.0000
MOZAMBIQUE               -0.28761679 0.28257 1.00000  1.0000
SOUTH AFRICA             -0.86814954 0.04126 0.33004  1.0000
LESOTHO                  -0.29841469 0.27531 0.55062  1.0000
BOTSWANA                  0.04090396 0.46740 1.00000  1.0000
SWAZILAND                -0.65938417 0.09362 0.28087  1.0000
MOROCCO                   0.02191606 0.48252 1.00000  1.0000
ALGERIA                  -0.36307938 0.23387 1.00000  1.0000
TUNISIA                   0.57910139 0.12339 0.37017  1.0000
LIBYA                     2.55272169 1.7e-07 1.2e-06 6.9e-06
SUDAN                     4.03925235 3.3e-16 3.0e-15 1.4e-14
EGYPT                     4.42133637 < 2e-16 < 2e-16 < 2e-16
> 
> 
> 
> cleanEx(); ..nameEx <- "plot.nb"
> 
> ### * plot.nb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: plot.nb
> ### Title: Plot a neighbours list
> ### Aliases: plot.nb plot.listw
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> plot(col.gal.nb, coords)
> title(main="GAL order 1 links with first nearest neighbours in red")
> col.knn <- knearneigh(coords, k=1)
> plot(knn2nb(col.knn), coords, add=TRUE, col="red", length=0.08)
> 
> 
> 
> cleanEx(); ..nameEx <- "poly2nb"
> 
> ### * poly2nb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: poly2nb
> ### Title: Construct neighbours list from polygon list
> ### Aliases: poly2nb
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> xx <- poly2nb(polys)
> dxx <- diffnb(xx, col.gal.nb)
Neighbour difference for region id: 1007 in relation to id: 1036 
Neighbour difference for region id: 1036 in relation to id: 1007 
Neighbour difference for region id: 1032 in relation to id: 1034 
Neighbour difference for region id: 1034 in relation to id: 1032 
Neighbour difference for region id: 1045 in relation to id: 1047 
Neighbour difference for region id: 1047 in relation to id: 1045 
> library(maptools)
> plot(polys, border="grey", forcefill=FALSE)
> plot(col.gal.nb, coords, add=TRUE)
> plot(dxx, coords, add=TRUE, col="red")
> title(main="Differences (red) in Columbus GAL weights (black)\nand polygon generated queen weights")
> xxx <- poly2nb(polys, queen=FALSE)
> dxxx <- diffnb(xxx, col.gal.nb)
Neighbour difference for region id: 1003 in relation to id: 1039 
Neighbour difference for region id: 1018 in relation to id: 1032 
Neighbour difference for region id: 1010 in relation to id: 1019 
Neighbour difference for region id: 1039 in relation to id: 1003 
Neighbour difference for region id: 1019 in relation to id: 1010 
Neighbour difference for region id: 1035 in relation to id: 1033 
Neighbour difference for region id: 1032 in relation to id: 1018 1031 
Neighbour difference for region id: 1020 in relation to id: 1033 
Neighbour difference for region id: 1031 in relation to id: 1032 1030 
Neighbour difference for region id: 1033 in relation to id: 1035 1020 
Neighbour difference for region id: 1023 in relation to id: 1029 
Neighbour difference for region id: 1030 in relation to id: 1031 
Neighbour difference for region id: 1029 in relation to id: 1023 
> plot(polys, border = "grey", forcefill=FALSE)
> plot(col.gal.nb, coords, add = TRUE)
> plot(dxxx, coords, add = TRUE, col = "red")
> title(main="Differences (red) in Columbus GAL weights (black)\nand polygon generated rook weights")
> cards <- card(xx)
> maxconts <- which(cards == max(cards))
> if(length(maxconts) > 1) maxconts <- maxconts[1]
> fg <- rep("grey", length(polys))
> fg[maxconts] <- "red"
> fg[xx[[maxconts]]] <- "green"
> plot(polys, col=fg, forcefill=FALSE)
> title(main="Region with largest number of contiguities")
> 
> 
> 
> cleanEx(); ..nameEx <- "predict.sarlm"
> 
> ### * predict.sarlm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: predict.sarlm
> ### Title: Prediction for spatial simultaneous autoregressive linear model
> ###   objects
> ### Aliases: predict.sarlm print.sarlm.pred
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> COL.lag.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb))
> COL.mix.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb),
+   type="mixed")
> COL.err.eig <- errorsarlm(CRIME ~ INC + HOVAL, data=COL.OLD, nb2listw(COL.nb))
> print(p1 <- predict(COL.mix.eig))
           fit      trend    signal
1001 26.044311 14.8543508 11.189960
1002 44.034234 29.2632112 14.771023
1003 43.511934 25.8193818 17.692553
1004 37.656561 16.4555583 21.201002
1005 10.902976  0.3664066 10.536570
1006 36.829798 24.2905246 12.539274
1007 44.290467 27.0386615 17.251806
1008 38.853571 21.5342393 17.319331
1009 50.870854 29.5092783 21.361576
1010 16.401300  5.6029104 10.798389
1011 36.354390 28.6415353  7.712855
1012 20.452836 12.4607277  7.992108
1013 20.324088 14.4173433  5.906745
1014 19.243496 10.2606419  8.982854
1015 19.747775 12.2556861  7.492089
1016  6.962527 -2.0137491  8.976276
1017  7.452143 -6.3808928 13.833036
1018 28.481587 14.2125594 14.269028
1019 43.351392 28.0442064 15.307186
1020 50.359682 30.6608153 19.698867
1021 38.905226 24.7490977 14.156128
1022 44.724478 28.8314299 15.893048
1023 37.888974 23.7778863 14.111087
1024 45.527017 26.9163190 18.610698
1025 32.429571 17.1892401 15.240331
1026 26.490842 14.8893980 11.601444
1027 35.629158 23.4577209 12.171437
1028 35.574326 21.9001006 13.674226
1029 38.598639 23.1818442 15.416795
1030 36.602053 14.8614072 21.740646
1031 50.320031 30.1013982 20.218633
1032 53.698863 31.2094168 22.489447
1033 49.364208 26.5151201 22.849088
1034 46.262357 25.5538226 20.708534
1035 39.177121 15.7689329 23.408188
1036 54.984344 32.6590841 22.325260
1037 51.611458 33.1290203 18.482438
1038 51.998831 30.7428313 21.256000
1039 43.651605 27.4107880 16.240817
1040 44.196841 25.9409252 18.255916
1041 49.310592 29.5106497 19.799943
1042 37.995310 15.7039024 22.291408
1043 46.908709 28.2687603 18.639948
1044 28.976789 19.5389223  9.437867
1045 25.343793 17.1838200  8.159973
1046 24.006252 16.0103703  7.995882
1047 25.034907 18.4616473  6.573260
1048 10.478529  3.3573578  7.121171
1049 13.495623  5.3356502  8.159973
> print(p2 <- predict(COL.mix.eig, newdata=COL.OLD, listw=nb2listw(COL.nb)))
           fit      trend    signal
1001 29.038788 14.8543508 14.184437
1002 46.227075 29.2632112 16.963864
1003 45.640479 25.8193818 19.821097
1004 36.643520 16.4555583 20.187962
1005 14.819940  0.3664066 14.453533
1006 38.764777 24.2905246 14.474252
1007 45.715716 27.0386615 18.677055
1008 37.514611 21.5342393 15.980372
1009 49.324228 29.5092783 19.814950
1010 17.510607  5.6029104 11.907696
1011 34.973608 28.6415353  6.332072
1012 21.079100 12.4607277  8.618372
1013 19.704134 14.4173433  5.286791
1014 16.365521 10.2606419  6.104879
1015 17.063856 12.2556861  4.808170
1016  6.190282 -2.0137491  8.204031
1017  5.967260 -6.3808928 12.348153
1018 29.250462 14.2125594 15.037902
1019 41.530036 28.0442064 13.485830
1020 49.344770 30.6608153 18.683954
1021 39.508818 24.7490977 14.759720
1022 42.772692 28.8314299 13.941262
1023 37.114901 23.7778863 13.337015
1024 43.622499 26.9163190 16.706180
1025 33.247197 17.1892401 16.057957
1026 30.301331 14.8893980 15.411933
1027 38.316063 23.4577209 14.858342
1028 36.886068 21.9001006 14.985967
1029 38.970564 23.1818442 15.788720
1030 33.014615 14.8614072 18.153208
1031 48.209875 30.1013982 18.108477
1032 50.808064 31.2094168 19.598647
1033 44.555996 26.5151201 18.040876
1034 43.232773 25.5538226 17.678951
1035 35.009061 15.7689329 19.240128
1036 52.113364 32.6590841 19.454280
1037 52.189015 33.1290203 19.059995
1038 51.631805 30.7428313 20.888973
1039 46.543565 27.4107880 19.132776
1040 45.036095 25.9409252 19.095170
1041 45.907835 29.5106497 16.397185
1042 35.337110 15.7039024 19.633208
1043 43.948398 28.2687603 15.679638
1044 32.091257 19.5389223 12.552334
1045 29.647005 17.1838200 12.463185
1046 26.375304 16.0103703 10.364934
1047 27.235807 18.4616473  8.774160
1048 14.785518  3.3573578 11.428160
1049 17.798835  5.3356502 12.463185
> AIC(COL.mix.eig)
[1] 376.787
> sqrt(deviance(COL.mix.eig)/length(COL.nb))
[1] 9.580773
> sqrt(sum((COL.OLD$CRIME - as.vector(p1))^2)/length(COL.nb))
[1] 9.580773
> sqrt(sum((COL.OLD$CRIME - as.vector(p2))^2)/length(COL.nb))
[1] 10.35029
> AIC(COL.err.eig)
[1] 376.7609
> sqrt(deviance(COL.err.eig)/length(COL.nb))
[1] 9.776221
> sqrt(sum((COL.OLD$CRIME - as.vector(predict(COL.err.eig)))^2)/length(COL.nb))
[1] 9.776221
> sqrt(sum((COL.OLD$CRIME - as.vector(predict(COL.err.eig, newdata=COL.OLD,
+   listw=nb2listw(COL.nb))))^2)/length(COL.nb))
[1] 11.61744
> AIC(COL.lag.eig)
[1] 374.7809
> sqrt(deviance(COL.lag.eig)/length(COL.nb))
[1] 9.772129
> sqrt(sum((COL.OLD$CRIME - as.vector(predict(COL.lag.eig)))^2)/length(COL.nb))
[1] 9.772129
> sqrt(sum((COL.OLD$CRIME - as.vector(predict(COL.lag.eig, newdata=COL.OLD,
+   listw=nb2listw(COL.nb))))^2)/length(COL.nb))
[1] 10.72654
> 
> 
> 
> cleanEx(); ..nameEx <- "probmap"
> 
> ### * probmap
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: probmap
> ### Title: Probability mapping for rates
> ### Aliases: probmap
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(auckland)
> res <- probmap(auckland$Deaths.1977.85, 9*auckland$Under.5.1981)
> brks <- c(-Inf,2,2.5,3,3.5,Inf)
> cols <- grey(6:2/7)
> library(maptools)
> plot(auckpolys, col=cols[findInterval(res$raw*1000, brks)], forcefill=FALSE)
> legend(c(70,90), c(70,95), fill=cols, legend=leglabs(brks), bty="n")
> title(main="Crude (raw) estimates of infant mortality per 1000 per year")
> brks <- c(-Inf,47,83,118,154,190,Inf)
> cols <- cm.colors(6)
> plot(auckpolys, col=cols[findInterval(res$relRisk, brks)], forcefill=FALSE)
> legend(c(70,90), c(70,95), fill=cols, legend=leglabs(brks), bty="n")
> title(main="Standardised mortality ratios for Auckland child deaths")
> brks <- c(0,0.05,0.1,0.2,0.8,0.9,0.95,1)
> cols <- cm.colors(7)
> plot(auckpolys, col=cols[findInterval(res$pmap, brks)], forcefill=FALSE)
> legend(c(70,90), c(70,95), fill=cols, legend=leglabs(brks), bty="n")
> title(main="Poisson probabilities for Auckland child mortality")
> 
> 
> 
> cleanEx(); ..nameEx <- "read.gal"
> 
> ### * read.gal
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: read.gal
> ### Title: Read a GAL lattice file into a neighbours list
> ### Aliases: read.gal read.geoda
> ### Keywords: spatial
> 
> ### ** Examples
> 
> us48.fipsno <- read.geoda(system.file("etc/weights/us48.txt",
+  package="spdep")[1])
> us48.q <- read.gal(system.file("etc/weights/us48_q.GAL", package="spdep")[1],
+  us48.fipsno$Fipsno)
> us48.r <- read.gal(system.file("etc/weights/us48_rk.GAL", package="spdep")[1],
+  us48.fipsno$Fipsno)
> data(state)
> if (as.numeric(paste(version$major, version$minor, sep="")) < 19) {
+  m50.48 <- match(us48.fipsno$"State.name", state.name)
+ } else {
+  m50.48 <- match(us48.fipsno$"State_name", state.name)
+ }
> plot(us48.q, as.matrix(as.data.frame(state.center))[m50.48,])
> plot(diffnb(us48.r, us48.q),
+  as.matrix(as.data.frame(state.center))[m50.48,], add=TRUE, col="red")
Neighbour difference for region id: 4 in relation to id: 8 
Neighbour difference for region id: 8 in relation to id: 4 
Neighbour difference for region id: 35 in relation to id: 49 
Neighbour difference for region id: 49 in relation to id: 35 
> title(main="Differences between rook and queen criteria imported neighbours lists")
> 
> 
> 
> cleanEx(); ..nameEx <- "read.gwt2nb"
> 
> ### * read.gwt2nb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: read.gwt2nb
> ### Title: Read and write spatial neighbour files
> ### Aliases: read.gwt2nb write.sn2gwt read.dat2listw write.sn2dat
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(baltimore)
> STATION <- baltimore$STATION
> gwt1 <- read.gwt2nb(system.file("etc/weights/baltk4.GWT", package="spdep")[1],
+  STATION)
Warning in read.gwt2nb(system.file("etc/weights/baltk4.GWT", package = "spdep")[1],  : 
	 102, 115, 208 are not destinations
> cat(paste("Neighbours list symmetry;", is.symmetric.nb(gwt1, FALSE, TRUE),
+  "\n"))
Neighbours list symmetry; FALSE 
> listw1 <- nb2listw(gwt1, style="B", glist=attr(gwt1, "GeoDa")$dist)
> tmpGWT <- tempfile()
> write.sn2gwt(listw2sn(listw1), tmpGWT)
> gwt2 <- read.gwt2nb(tmpGWT, STATION)
Warning in read.gwt2nb(tmpGWT, STATION) : 102, 115, 208 are not destinations
> cat(paste("Neighbours list symmetry;", is.symmetric.nb(gwt2, FALSE, TRUE),
+  "\n"))
Neighbours list symmetry; FALSE 
> data(oldcol)
> diffnb(gwt1, gwt2)
> tmpMAT <- tempfile()
> COL.W <- nb2listw(COL.nb)
> write.sn2dat(listw2sn(COL.W), tmpMAT)
> listwmat1 <- read.dat2listw(tmpMAT)
> diffnb(listwmat1$neighbours, COL.nb, verbose=TRUE)
Warning in diffnb(listwmat1$neighbours, COL.nb, verbose = TRUE) : 
	 region.id differ; using ids of first list
> listwmat2 <- read.dat2listw(system.file("etc/weights/wmat.dat", 
+  package="spdep")[1])
> diffnb(listwmat1$neighbours, listwmat2$neighbours, verbose=TRUE)
> 
> 
> 
> cleanEx(); ..nameEx <- "set.spChkOption"
> 
> ### * set.spChkOption
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: set.spChkOption
> ### Title: Control checking of spatial object IDs
> ### Aliases: set.spChkOption get.spChkOption chkIDs spNamedVec
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> rownames(COL.OLD)
 [1] "1001" "1002" "1003" "1004" "1005" "1006" "1007" "1008" "1009" "1010"
[11] "1011" "1012" "1013" "1014" "1015" "1016" "1017" "1018" "1019" "1020"
[21] "1021" "1022" "1023" "1024" "1025" "1026" "1027" "1028" "1029" "1030"
[31] "1031" "1032" "1033" "1034" "1035" "1036" "1037" "1038" "1039" "1040"
[41] "1041" "1042" "1043" "1044" "1045" "1046" "1047" "1048" "1049"
> data(columbus)
> rownames(columbus)
 [1] "1005" "1001" "1006" "1002" "1007" "1008" "1004" "1003" "1018" "1010"
[11] "1038" "1037" "1039" "1040" "1009" "1036" "1011" "1042" "1041" "1017"
[21] "1043" "1019" "1012" "1035" "1032" "1020" "1021" "1031" "1033" "1034"
[31] "1045" "1013" "1022" "1044" "1023" "1046" "1030" "1024" "1047" "1016"
[41] "1014" "1049" "1029" "1025" "1028" "1048" "1015" "1027" "1026"
> get.spChkOption()
[1] FALSE
> oldChk <- set.spChkOption(TRUE)
> get.spChkOption()
[1] TRUE
> chkIDs(COL.OLD, nb2listw(COL.nb))
[1] TRUE
> chkIDs(columbus, nb2listw(col.gal.nb))
[1] TRUE
> chkIDs(columbus, nb2listw(COL.nb))
[1] FALSE
> tmp <- try(moran.test(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb)))
> print(tmp)

	Moran's I test under randomisation

data:  spNamedVec("CRIME", COL.OLD)  
weights: nb2listw(COL.nb)  
 
Moran I statistic standard deviate = 5.6341, p-value = 8.797e-09
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.510951264      -0.020833333       0.008908762 

> tmp <- try(moran.test(spNamedVec("CRIME", columbus), nb2listw(col.gal.nb)))
> print(tmp)

	Moran's I test under randomisation

data:  spNamedVec("CRIME", columbus)  
weights: nb2listw(col.gal.nb)  
 
Moran I statistic standard deviate = 5.3427, p-value = 4.578e-08
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.485770914      -0.020833333       0.008991121 

> tmp <- try(moran.test(spNamedVec("CRIME", columbus), nb2listw(COL.nb)))
Error in moran.test(spNamedVec("CRIME", columbus), nb2listw(COL.nb)) : 
	Check of data and weights ID integrity failed
> print(tmp)
[1] "Error in moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb)) : \n\tCheck of data and weights ID integrity failed\n"
attr(,"class")
[1] "try-error"
> set.spChkOption(FALSE)
[1] TRUE
> get.spChkOption()
[1] FALSE
> moran.test(spNamedVec("CRIME", columbus), nb2listw(COL.nb))

	Moran's I test under randomisation

data:  spNamedVec("CRIME", columbus)  
weights: nb2listw(COL.nb)  
 
Moran I statistic standard deviate = 3.8402, p-value = 6.147e-05
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.341628707      -0.020833333       0.008908762 

> tmp <- try(moran.test(spNamedVec("CRIME", columbus), nb2listw(COL.nb),
+  spChk=TRUE))
Error in moran.test(spNamedVec("CRIME", columbus), nb2listw(COL.nb), spChk = TRUE) : 
	Check of data and weights ID integrity failed
> print(tmp)
[1] "Error in moran.test(spNamedVec(\"CRIME\", columbus), nb2listw(COL.nb), spChk = TRUE) : \n\tCheck of data and weights ID integrity failed\n"
attr(,"class")
[1] "try-error"
> set.spChkOption(oldChk)
[1] FALSE
> get.spChkOption()
[1] FALSE
> 
> 
> 
> cleanEx(); ..nameEx <- "similar.listw"
> 
> ### * similar.listw
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: similar.listw
> ### Title: Create symmetric similar weights lists
> ### Aliases: similar.listw
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> COL.W <- nb2listw(COL.nb, style="W")
> COL.S <- nb2listw(COL.nb, style="S")
> log(prod(1 - 0.5 * eigenw(COL.W)))
[1] -1.627660
> log(prod(1 - 0.5 * eigenw(similar.listw(COL.W))))
[1] -1.627660
> Det <- getMethod("det", "matrix.csr")
> log(Det(asMatrixCsrIrW(asMatrixCsrListw(similar.listw(COL.W)), 0.5)))
[1] -1.627660
> log(prod(1 - 0.5 * eigenw(COL.S)))
[1] -1.602757
> log(prod(1 - 0.5 * eigenw(similar.listw(COL.S))))
[1] -1.602757
> log(Det(asMatrixCsrIrW(asMatrixCsrListw(similar.listw(COL.S)), 0.5)))
[1] -1.602757
> 
> 
> 
> cleanEx(); ..nameEx <- "sp.correlogram"
> 
> ### * sp.correlogram
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sp.correlogram
> ### Title: Spatial correlogram
> ### Aliases: sp.correlogram plot.spcor print.spcor
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(nc.sids)
> ft.SID74 <- sqrt(1000)*(sqrt(nc.sids$SID74/nc.sids$BIR74) +
+   sqrt((nc.sids$SID74+1)/nc.sids$BIR74))
> tr.SIDS74 <- ft.SID74*sqrt(nc.sids$BIR74)
> names(tr.SIDS74) <- rownames(nc.sids)
> print(sp.correlogram(ncCC89.nb, tr.SIDS74, order=8, method="corr",
+  zero.policy=TRUE))
Spatial correlogram for tr.SIDS74 
method: Spatial autocorrelation 
          1           2           3           4           5           6 
 0.38193491  0.47679881  0.11740653  0.09935901  0.27819159  0.30153012 
          7           8 
-0.05150923  0.05283813 
> print(sp.correlogram(ncCC89.nb, tr.SIDS74, order=8, method="I",
+  zero.policy=TRUE))
Spatial correlogram for tr.SIDS74 
method: Moran's I 
      estimate expectation    variance
1  0.231168467 -0.01030928 0.005537764
2  0.224693022 -0.01030928 0.003781723
3  0.019357594 -0.01030928 0.002938570
4  0.004225498 -0.01030928 0.002497404
5  0.087554814 -0.01030928 0.002287489
6  0.075836203 -0.01030928 0.002158346
7 -0.075224296 -0.01030928 0.002228181
8 -0.026106302 -0.01030928 0.002521056
> plot(sp.correlogram(ncCC89.nb, tr.SIDS74, order=8, method="I",
+  zero.policy=TRUE))
> plot(sp.correlogram(ncCC89.nb, tr.SIDS74, order=8, method="corr",
+  zero.policy=TRUE))
> drop.no.neighs <- !(1:length(ncCC89.nb) %in% which(card(ncCC89.nb) == 0))
> sub.ncCC89.nb <- subset(ncCC89.nb, drop.no.neighs)
> plot(sp.correlogram(sub.ncCC89.nb, subset(tr.SIDS74,  drop.no.neighs),
+  order=8, method="corr"))
> 
> 
> 
> cleanEx(); ..nameEx <- "sp.mantel.mc"
> 
> ### * sp.mantel.mc
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: sp.mantel.mc
> ### Title: Mantel-Hubert spatial general cross product statistic
> ### Aliases: sp.mantel.mc plot.mc.sim
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> sim1 <- sp.mantel.mc(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb),
+  nsim=99, type="geary", alternative="less")
> sim1

	Mantel permutation test for geary measure

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(COL.nb) 
number of simulations + 1: 100 
 
statistic = 51.9273, observed rank = 1, p-value = 0.01
alternative hypothesis: less 
sample estimates:
mean of permutations   sd of permutations 
           97.467742             7.576027 

> plot(sim1)
> sp.mantel.mc(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb), nsim=99,
+  type="sokal", alternative="less")

	Mantel permutation test for sokal measure

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(COL.nb) 
number of simulations + 1: 100 
 
statistic = 36.6946, observed rank = 1, p-value = 0.01
alternative hypothesis: less 
sample estimates:
mean of permutations   sd of permutations 
           55.979566             3.252045 

> sp.mantel.mc(spNamedVec("CRIME", COL.OLD), nb2listw(COL.nb), nsim=99,
+  type="moran")

	Mantel permutation test for moran measure

data:  spNamedVec("CRIME", COL.OLD) 
weights: nb2listw(COL.nb) 
number of simulations + 1: 100 
 
statistic = 24.5257, observed rank = 100, p-value = 0.01
alternative hypothesis: greater 
sample estimates:
mean of permutations   sd of permutations 
          -0.5243846            4.5409376 

> 
> 
> 
> cleanEx(); ..nameEx <- "spweights.constants"
> 
> ### * spweights.constants
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: spweights.constants
> ### Title: Provides constants for spatial weights matrices
> ### Aliases: spweights.constants Szero
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> B <- spweights.constants(nb2listw(COL.nb, style="B"))
> W <- spweights.constants(nb2listw(COL.nb, style="W"))
> C <- spweights.constants(nb2listw(COL.nb, style="C"))
> S <- spweights.constants(nb2listw(COL.nb, style="S"))
> U <- spweights.constants(nb2listw(COL.nb, style="U"))
> print(data.frame(rbind(unlist(B), unlist(W), unlist(C), unlist(S), unlist(U)),
+   row.names=c("B", "W", "C", "S", "U")))
   n n1 n2 n3   nn  S0           S1           S2
B 49 48 47 46 2401 232 464.00000000 5.136000e+03
W 49 48 47 46 2401  49  23.29434146 2.048729e+02
C 49 48 47 46 2401  49  20.69827586 2.291085e+02
S 49 48 47 46 2401  49  21.25561347 2.134568e+02
U 49 48 47 46 2401   1   0.00862069 9.542212e-02
> 
> 
> 
> cleanEx(); ..nameEx <- "subset.listw"
> 
> ### * subset.listw
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: subset.listw
> ### Title: Subset a spatial weights list
> ### Aliases: subset.listw
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> to.be.dropped <- c(31, 34, 36, 39, 42, 46)
> pre <- nb2listw(col.gal.nb)
> print(pre)
Characteristics of weights list object:
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 230 
Percentage nonzero weights: 9.579342 
Average number of links: 4.693878 

Weights style: W 
Weights constants summary:
   n   nn S0       S1       S2
W 49 2401 49 23.48489 204.6687
> post <- subset(pre, !(1:length(col.gal.nb) %in% to.be.dropped))
> print(post)
Characteristics of weights list object:
Neighbour list object:
Number of regions: 43 
Number of nonzero links: 212 
Percentage nonzero weights: 11.46566 
Average number of links: 4.930233 

Weights style: W 
Weights constants summary:
   n   nn S0       S1       S2
W 43 1849 43 19.26584 178.4604
> 
> 
> 
> cleanEx(); ..nameEx <- "subset.nb"
> 
> ### * subset.nb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: subset.nb
> ### Title: Subset a neighbours list
> ### Aliases: subset.nb
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> plot(col.gal.nb, coords)
> to.be.dropped <- c(31, 34, 36, 39, 42, 46)
> text(coords[to.be.dropped,1], coords[to.be.dropped,2], labels=to.be.dropped,
+   pos=2, offset=0.3)
> sub.col.gal.nb <- subset(col.gal.nb,
+   !(1:length(col.gal.nb) %in% to.be.dropped))
> plot(sub.col.gal.nb, coords[-to.be.dropped,], col="red", add=TRUE)
> which(!(attr(col.gal.nb, "region.id") %in%
+   attr(sub.col.gal.nb, "region.id")))
[1] 31 34 36 39 42 46
> 
> 
> 
> cleanEx(); ..nameEx <- "summary.nb"
> 
> ### * summary.nb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.nb
> ### Title: Print and summary function for neighbours and weights lists
> ### Aliases: summary.nb print.nb summary.listw print.listw
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> col.gal.nb
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 230 
Percentage nonzero weights: 9.579342 
Average number of links: 4.693878 
> summary(col.gal.nb, coords)
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 230 
Percentage nonzero weights: 9.579342 
Average number of links: 4.693878 
Link number distribution:

 2  3  4  5  6  7  8  9 10 
 7  7 13  4  9  6  1  1  1 
7 least connected regions:
1005 1008 1045 1047 1049 1048 1015 with 2 links
1 most connected region:
1017 with 10 links
Summary of link distances:
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
 0.1276  0.3613  0.4566  0.4694  0.5536  0.8924 

  The decimal point is 1 digit(s) to the left of the |

  1 | 3344
  1 | 99
  2 | 000011333344
  2 | 556677779999
  3 | 000011222222223344444444
  3 | 556666777777888888889999999999
  4 | 00001111112233333333334444
  4 | 55666666666666777777777788888899
  5 | 0011112222222222222233334444
  5 | 556666667788
  6 | 000000112244
  6 | 5577889999
  7 | 11112244
  7 | 557777
  8 | 1144
  8 | 55999999

> col.listw <- nb2listw(col.gal.nb, style="W")
> col.listw
Characteristics of weights list object:
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 230 
Percentage nonzero weights: 9.579342 
Average number of links: 4.693878 

Weights style: W 
Weights constants summary:
   n   nn S0       S1       S2
W 49 2401 49 23.48489 204.6687
> summary(col.listw)
Characteristics of weights list object:
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 230 
Percentage nonzero weights: 9.579342 
Average number of links: 4.693878 
Link number distribution:

 2  3  4  5  6  7  8  9 10 
 7  7 13  4  9  6  1  1  1 
7 least connected regions:
1005 1008 1045 1047 1049 1048 1015 with 2 links
1 most connected region:
1017 with 10 links

Weights style: W 
Weights constants summary:
   n   nn S0       S1       S2
W 49 2401 49 23.48489 204.6687
> 
> 
> 
> cleanEx(); ..nameEx <- "summary.sarlm"
> 
> ### * summary.sarlm
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: summary.sarlm
> ### Title: summary method for class sarlm
> ### Aliases: summary.sarlm print.sarlm print.summary.sarlm
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(oldcol)
> COL.mix.eig <- lagsarlm(CRIME ~ INC + HOVAL, data=COL.OLD,
+  nb2listw(COL.nb), type="mixed", method="eigen", quiet=FALSE)

Spatial mixed autoregressive model
Jacobian calculated using neighbourhood matrix eigenvalues
Computing eigenvalues ...

(eigen) rho:	 -0.5674437 	function value:	 -193.3853 
(eigen) rho:	 0.03126655 	function value:	 -183.7273 
(eigen) rho:	 0.4012898 	function value:	 -181.4045 
(eigen) rho:	 0.5248287 	function value:	 -181.5759 
(eigen) rho:	 0.4184076 	function value:	 -181.3946 
(eigen) rho:	 0.4255293 	function value:	 -181.3935 
(eigen) rho:	 0.4263929 	function value:	 -181.3935 
(eigen) rho:	 0.426337 	function value:	 -181.3935 
(eigen) rho:	 0.4263355 	function value:	 -181.3935 
(eigen) rho:	 0.4263355 	function value:	 -181.3935 
(eigen) rho:	 0.4263355 	function value:	 -181.3935 
> summary(COL.mix.eig, correlation=TRUE)

Call:
lagsarlm(formula = CRIME ~ INC + HOVAL, data = COL.OLD, listw = nb2listw(COL.nb), 
    type = "mixed", method = "eigen", quiet = FALSE)

Residuals:
      Min        1Q    Median        3Q       Max 
-37.47829  -6.46731  -0.33835   6.05200  22.62969 

Type: mixed 
Coefficients: (asymptotic standard errors) 
             Estimate Std. Error z value  Pr(>|z|)
(Intercept) 42.822415  12.667205  3.3806 0.0007233
INC         -0.914223   0.331094 -2.7612 0.0057586
HOVAL       -0.293738   0.089212 -3.2926 0.0009927
lag.INC     -0.520284   0.565129 -0.9206 0.3572355
lag.HOVAL    0.245640   0.178917  1.3729 0.1697756

Rho: 0.42634 LR test value: 5.3693 p-value: 0.020494 
Asymptotic standard error: 0.15623 z-value: 2.7288 p-value: 0.0063561 
Wald statistic: 7.4465 p-value: 0.0063561 

Log likelihood: -181.3935 for mixed model
ML residual variance (sigma squared): 91.791, (sigma: 9.5808)
Number of observations: 49 
Number of parameters estimated: 7 
AIC: 376.79, (AIC for lm: 380.16)
LM test for residual autocorrelation
test value: 0.28919 p-value: 0.59074 

Correlation of Coefficients:
            sigma rho   (Intercept) INC   HOVAL lag.INC
rho         -0.18                                      
(Intercept)  0.16 -0.89                                
INC         -0.03  0.14 -0.19                          
HOVAL        0.02 -0.09  0.03       -0.45              
lag.INC     -0.09  0.49 -0.53       -0.36  0.05        
lag.HOVAL   -0.04  0.19 -0.36        0.19 -0.24 -0.41  

> 
> 
> 
> cleanEx(); ..nameEx <- "testnb"
> 
> ### * testnb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: is.symmetric.nb
> ### Title: Test a neighbours list for symmetry
> ### Aliases: is.symmetric.nb sym.attr.nb make.sym.nb is.symmetric.glist
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> print(is.symmetric.nb(col.gal.nb, verbose=TRUE, force=TRUE))
[1] TRUE
> k4 <- knn2nb(knearneigh(coords, k=4), row.names=rownames(columbus))
> k4 <- sym.attr.nb(k4)
> print(is.symmetric.nb(k4))
Non-symmetric neighbours list
[1] FALSE
> k4.sym <- make.sym.nb(k4)
> print(is.symmetric.nb(k4.sym))
[1] TRUE
> 
> 
> 
> cleanEx(); ..nameEx <- "tri2nb"
> 
> ### * tri2nb
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: tri2nb
> ### Title: Neighbours list from tri object
> ### Aliases: tri2nb
> ### Keywords: spatial
> 
> ### ** Examples
> 
> require(tripack)
[1] TRUE
> data(columbus)
> col.tri.nb <- tri2nb(coords, row.names=rownames(columbus))
> library(maptools)
> plot(polys, border="grey", forcefill=FALSE)
> plot(col.tri.nb, coords, add=TRUE)
> title(main="Raw triangulation links")
> x <- seq(0,1,0.1)
> y <- seq(0,2,0.2)
> xy <- expand.grid(x, y)
> try(xy.nb <- tri2nb(xy))
Error in tri.mesh(x = coords[, 1], y = coords[, 2]) : 
	error in trmesh
> seed <- 1234
> xid <- sample(1:nrow(xy))
> xy.nb <- tri2nb(xy[xid,])
> plot(xy.nb, xy[xid,])
> 
> 
> 
> cleanEx(); ..nameEx <- "used.cars"
> 
> ### * used.cars
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: used.cars
> ### Title: US 1960 used car prices
> ### Aliases: used.cars usa48.nb
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data(used.cars)
> moran.test(spNamedVec("price.1960", used.cars), nb2listw(usa48.nb))

	Moran's I test under randomisation

data:  spNamedVec("price.1960", used.cars)  
weights: nb2listw(usa48.nb)  
 
Moran I statistic standard deviate = 8.1752, p-value < 2.2e-16
alternative hypothesis: greater 
sample estimates:
Moran I statistic       Expectation          Variance 
      0.783561543      -0.021276596       0.009692214 

> moran.plot(spNamedVec("price.1960", used.cars), nb2listw(usa48.nb),
+   labels=rownames(used.cars))
Potentially influential observations of
	 lm(formula = wx ~ x) :

   dfb.1_ dfb.x dffit cov.r   cook.d hat  
ID  0.01  -0.01 -0.01  1.15_*  0.00   0.09
UT -0.07   0.07  0.08  1.13_*  0.00   0.08
WA -0.27   0.29  0.45  0.86_*  0.09   0.03
WI  0.38  -0.36  0.51  0.86_*  0.12   0.04
WY  0.08  -0.08 -0.09  1.14_*  0.00   0.09
> uc.lm <- lm(price.1960 ~ tax.charges, data=used.cars)
> summary(uc.lm)

Call:
lm(formula = price.1960 ~ tax.charges, data = used.cars)

Residuals:
     Min       1Q   Median       3Q      Max 
-116.701  -45.053   -1.461   43.400  107.807 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept) 1435.7506    27.5796  52.058  < 2e-16 ***
tax.charges    0.6872     0.1754   3.918 0.000294 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 

Residual standard error: 57.01 on 46 degrees of freedom
Multiple R-Squared: 0.2503,	Adjusted R-squared: 0.234 
F-statistic: 15.35 on 1 and 46 DF,  p-value: 0.0002939 

> lm.morantest(uc.lm, nb2listw(usa48.nb))

	Global Moran's I for regression residuals

data:  
model: lm(formula = price.1960 ~ tax.charges, data = used.cars)
weights: nb2listw(usa48.nb)
 
Moran I statistic standard deviate = 6.3869, p-value = 8.466e-11
alternative hypothesis: greater 
sample estimates:
Observed Moran's I        Expectation           Variance 
       0.574817771       -0.030300549        0.008976437 

> lm.morantest.sad(uc.lm, nb2listw(usa48.nb))

	Saddlepoint approximation for global Moran's I (Barndorff-Nielsen
	formula)

data:  
model:lm(formula = price.1960 ~ tax.charges, data = used.cars)
weights: nb2listw(usa48.nb)
 
Saddlepoint approximation = 5.6688, p-value = 7.19e-09
alternative hypothesis: greater 
sample estimates:
Observed Moran's I 
         0.5748178 

> lm.LMtests(uc.lm, nb2listw(usa48.nb))

	Lagrange multiplier diagnostics for spatial dependence

data:  
model: lm(formula = price.1960 ~ tax.charges, data = used.cars)
weights: nb2listw(usa48.nb)
 
LMerr = 31.7926, df = 1, p-value = 1.715e-08

> uc.err <- errorsarlm(price.1960 ~ tax.charges, data=used.cars,
+   nb2listw(usa48.nb), tol.solve=1.0e-13, tol.opt=.Machine$double.eps^0.3)
> summary(uc.err)

Call:errorsarlm(formula = price.1960 ~ tax.charges, data = used.cars, 
    listw = nb2listw(usa48.nb), tol.solve = 1e-13, tol.opt = .Machine$double.eps^0.3)

Residuals:
     Min       1Q   Median       3Q      Max 
-74.8241 -17.4590   2.4061  21.2784  64.5967 

Type: error 
Coefficients: (asymptotic standard errors) 
              Estimate Std. Error z value Pr(>|z|)
(Intercept) 1528.34521   31.96239 47.8170   <2e-16
tax.charges    0.08831    0.11923  0.7406   0.4589

Lambda: 0.81899 LR test value: 40.899 p-value: 1.6030e-10 
Asymptotic standard error: 0.074052 z-value: 11.06 p-value: < 2.22e-16 
Wald statistic: 122.32 p-value: < 2.22e-16 

Log likelihood: -240.7163 for error model
ML residual variance (sigma squared): 1043.9, (sigma: 32.309)
Number of observations: 48 
Number of parameters estimated: 4 
AIC: 489.43, (AIC for lm: 528.33)

> uc.lag <- lagsarlm(price.1960 ~ tax.charges, data=used.cars,
+   nb2listw(usa48.nb), tol.solve=1.0e-13, tol.opt=.Machine$double.eps^0.3)
> summary(uc.lag)

Call:lagsarlm(formula = price.1960 ~ tax.charges, data = used.cars, 
    listw = nb2listw(usa48.nb), tol.solve = 1e-13, tol.opt = .Machine$double.eps^0.3)

Residuals:
     Min       1Q   Median       3Q      Max 
-77.6781 -16.9505   4.2498  19.5486  58.9811 

Type: lag 
Coefficients: (asymptotic standard errors) 
             Estimate Std. Error z value Pr(>|z|)
(Intercept) 309.42997  123.03283  2.5150  0.01190
tax.charges   0.16711    0.10212  1.6364  0.10175

Rho: 0.78302 LR test value: 42.681 p-value: 6.4426e-11 
Asymptotic standard error: 0.081637 z-value: 9.5914 p-value: < 2.22e-16 
Wald statistic: 91.995 p-value: < 2.22e-16 

Log likelihood: -239.8252 for lag model
ML residual variance (sigma squared): 1036.7, (sigma: 32.197)
Number of observations: 48 
Number of parameters estimated: 4 
AIC: 487.65, (AIC for lm: 528.33)
LM test for residual autocorrelation
test value: 2.1139 p-value: 0.14596 

> uc.lag1 <- lagsarlm(price.1960 ~ 1, data=used.cars,
+   nb2listw(usa48.nb), tol.solve=1.0e-13, tol.opt=.Machine$double.eps^0.3)
> summary(uc.lag1)

Call:
lagsarlm(formula = price.1960 ~ 1, data = used.cars, listw = nb2listw(usa48.nb), 
    tol.solve = 1e-13, tol.opt = .Machine$double.eps^0.3)

Residuals:
    Min      1Q  Median      3Q     Max 
-76.152 -18.221   5.249  21.631  63.498 

Type: lag 
Coefficients: (asymptotic standard errors) 
            Estimate Std. Error z value Pr(>|z|)
(Intercept)   263.50     109.61  2.4038  0.01622

Rho: 0.82919 LR test value: 54.202 p-value: 1.8086e-13 
Asymptotic standard error: 0.070993 z-value: 11.68 p-value: < 2.22e-16 
Wald statistic: 136.42 p-value: < 2.22e-16 

Log likelihood: -240.977 for lag model
ML residual variance (sigma squared): 1045.4, (sigma: 32.333)
Number of observations: 48 
Number of parameters estimated: 3 
AIC: 487.95, (AIC for lm: 540.16)
LM test for residual autocorrelation
test value: 2.1495 p-value: 0.14262 

> uc.err1 <- errorsarlm(price.1960 ~ 1, data=used.cars,
+   nb2listw(usa48.nb), tol.solve=1.0e-13, tol.opt=.Machine$double.eps^0.3)
> summary(uc.err1)

Call:
errorsarlm(formula = price.1960 ~ 1, data = used.cars, listw = nb2listw(usa48.nb), 
    tol.solve = 1e-13, tol.opt = .Machine$double.eps^0.3)

Residuals:
    Min      1Q  Median      3Q     Max 
-76.152 -18.221   5.249  21.631  63.498 

Type: error 
Coefficients: (asymptotic standard errors) 
            Estimate Std. Error z value  Pr(>|z|)
(Intercept) 1542.607     27.321  56.462 < 2.2e-16

Lambda: 0.82919 LR test value: 54.202 p-value: 1.8086e-13 
Asymptotic standard error: 0.070993 z-value: 11.68 p-value: < 2.22e-16 
Wald statistic: 136.42 p-value: < 2.22e-16 

Log likelihood: -240.977 for error model
ML residual variance (sigma squared): 1045.4, (sigma: 32.333)
Number of observations: 48 
Number of parameters estimated: 3 
AIC: 487.95, (AIC for lm: 540.16)

> 
> 
> 
> cleanEx(); ..nameEx <- "write.nb.gal"
> 
> ### * write.nb.gal
> 
> flush(stderr()); flush(stdout())
> 
> ### Name: write.nb.gal
> ### Title: Write a neighbours list as a GAL lattice file
> ### Aliases: write.nb.gal
> ### Keywords: spatial
> 
> ### ** Examples
> 
> data(columbus)
> ind <- rownames(columbus)
> GALfile <- tempfile("GAL")
> write.nb.gal(col.gal.nb, GALfile, oldstyle=FALSE, ind="ind")
> col.queen <- read.gal(GALfile, region.id=ind)
> unlink(GALfile)
> summary(diffnb(col.queen, col.gal.nb))
Neighbour list object:
Number of regions: 49 
Number of nonzero links: 0 
Percentage nonzero weights: 0 
Average number of links: 0 
49 regions with no links:
1005 1001 1006 1002 1007 1008 1004 1003 1018 1010 1038 1037 1039 1040 1009 1036 1011 1042 1041 1017 1043 1019 1012 1035 1032 1020 1021 1031 1033 1034 1045 1013 1022 1044 1023 1046 1030 1024 1047 1016 1014 1049 1029 1025 1028 1048 1015 1027 1026
Link number distribution:

 0 
49 
> 
> 
> 
> ### * <FOOTER>
> ###
> cat("Time elapsed: ", proc.time() - get("ptime", env = .CheckExEnv),"\n")
Time elapsed:  106.76 3.97 111.29 0.01 0 
> grDevices::dev.off()
null device 
          1 
> ###
> ### Local variables: ***
> ### mode: outline-minor ***
> ### outline-regexp: "\\(> \\)?### [*]+" ***
> ### End: ***
> quit('no')